Skip to main content
SpringerLink
Log in

Basic Notions of Algebra

  • Chapter
Algebra I

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS))

Abstract

This book aims to present a general survey of algebra, of its basic notions and main branches. Now what language should we choose for this? In reply to the question ‘What does mathematics study?’, it is hardly acceptable to answer ‘structures’ or ‘sets with specified relations’; for among the myriad conceivable structures or sets with specified relations, only a very small discrete subset is of real interest to mathematicians, and the whole point of the question is to understand the special value of this infinitesimal fraction dotted among the amorphous masses. In the same way, the meaning of a mathematical notion is by no means confined to its formal definition; in fact, it may be rather better expressed by a (generally fairly small) sample of the basic examples, which serve the mathematician as the motivation and the substantive definition, and at the same time as the real meaning of the notion.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. The life of plants, vol. 5, part 2, Prosveshchenie, Moscow, 1981 (in Russian)

    Google Scholar 

  2. Arnol’d, V.I.: Mathematical methods of classical mechanics, Nauka, Moscow 1974; English translation: Grad. Texts Math. 60, Springer-Verlag, Berlin Heidelberg New York 1978. Zbl. 386. 70001

    Google Scholar 

  3. Artin, E.: Geometric algebra, Interscience, New York 1957. Zbl. 77, 21; Russian translation: Moscow, Nauka 1969. Zbl. 174, 294

    Google Scholar 

  4. Atiyah, M.F.: K-theory, Benjamin, New York Amsterdam 1967. Zbl. 159, 533

    Google Scholar 

  5. Atiyah, M.F., Macdonald, M.F.: Introduction to commutative algebra, Addison-Wesley, Reading, Mass. 1969. Zbl. 175, 36

    Google Scholar 

  6. Atiyah, M.F. and others: Representation theory of Lie groups, Lond. Math. Soc. Lect. Notes 34, Cambridge Univ. Press, Cambridge New York 1979. Zbl. 426. 22014

    Google Scholar 

  7. Baer, R.: Linear algebra and projective geometry, Pure Appl. Math. Vol. II, Academic Press, New York 1952. Zbl. 49, 381

    Google Scholar 

  8. Barwise, J. and others: Handbook of mathematical logic, Stud. Logic Found. Math. 90, North-Holland, Amsterdam 1978. Zbl. 443. 03001

    Google Scholar 

  9. Besse, A. ed.: Géométrie riemannienne en dimension 4, Séminaire Arthur Besse 1978/1979, CEDIC, Paris 1981. Zbl. 472. 00010

    Google Scholar 

  10. Birkhoff, G.: Lattice theory, Amer. Math. Soc., New York 1940. Zbl. 33, 101

    Google Scholar 

  11. Bogolyubov, N.N.: The theory of symmetry of elementary particles, in High-energy physics and the theory of elementary particles, Naukova Dumka, Kiev 1967, 5–112 (in Russian)

    Google Scholar 

  12. Borel, A.: Linear algebraic groups, Benjamin, New York Amsterdam 1969. Zbl. 186, 332

    Google Scholar 

  13. Borel, A.: Arithmetic properties of linear algebraic groups, in Proc. Int. Congr. Math., Stockholm, 1962, Inst. Mittag-Leffler, Djursholm 1963, 10–22. Zbl. 134, 165

    Google Scholar 

  14. Borel, A., Serre, J-P.: Le théorème de Riemann-Roch, Bull. Soc. Math. Fr. 86, 97–136 (1959). Zbl. 91, 330

    Google Scholar 

  15. Borevich, Z.I., Shafarevich, I.R.: Number theory, Nauka, Moscow 1964. Zbl. 121, 42; English translation: Academic Press, New York London 1966. Zbl. 145, 49

    Google Scholar 

  16. Bourbaki, N.: Éléments de mathématiques, Algèbre, Chap. 1–3, Hermann, Paris 1942–1948. I: 1942, Zbl. 60, 68. III: 1948, Zbl. 33, 259

    Google Scholar 

  17. Bourbaki, N.: Éléments de mathématiques, Algèbre, Chap. 9, Hermann, Paris 1959. Zbl. 102, 255

    Google Scholar 

  18. Bourbaki, N.: Éléments de mathématiques, Groupes et algèbres de Lie, Chap. 4–6, Hermann, Paris 1968. Zbl. 186, 330

    Google Scholar 

  19. Bröcker, Th.: Differentiable germs and catastrophes, Cambridge Univ. Press, Cambridge New York 1975. Zbl. 302. 58006

    Google Scholar 

  20. Brown, K.S.: Cohomology of groups, Grad. Texts Math. 87, Springer-Verlag, Berlin Heidelberg New York 1982. Zbl. 584. 20036

    Google Scholar 

  21. Burnside, W.: Theory of groups of finite order, Cambridge Univ. Press, Cambridge 1897; Reprint: Dover, New York 1955. Zbl. 64, 251

    Google Scholar 

  22. Cartan, H., Eilenberg, S.: Homological algebra, Princeton Univ. Press, Princeton, New Jersey 1956. Zbl. 75, 243

    Google Scholar 

  23. Cassels, J.W.S., Fröhlich, A. eds.: Algebraic number theory, Academic Press, London 1967. Zbl. 153, 74

    Google Scholar 

  24. Chandler, B., Magnus, W.: The history of combinatorial group theory, Stud. Hist. Math. Phys. Sci. 9, Springer-Verlag, Berlin Heidelberg New York 1982. Zbl. 498. 20001

    Google Scholar 

  25. Chevalley, C.: Theory of Lie groups, Princeton Mathematical Series 8, Princeton Univ. Press, Princeton, New Jersey 1946

    MATH  Google Scholar 

  26. Chevalley, C.: Introduction to the theory of algebraic functions of one variable, Am. Math. Soc., New York 1951. Zbl. 45, 323

    Google Scholar 

  27. Chevalley, C.: Classification des groupes de Lie algébriques, Séminaire C. Chevalley 1956–58, Secrétariat mathématique, Paris 1958

    Google Scholar 

  28. Chevalley, C.: La théorie des groupes algébriques, Proc. Int. Congr. Math., Edinburgh 1958, Cambridge Univ. Press, Cambridge New York 1960, 53–68. Zbl. 121, 378

    Google Scholar 

  29. Clifford, W.K.: Mathematical papers, Macmillan, London 1882

    Google Scholar 

  30. Courant, R., Hilbert, D.: Methoden der mathematischen Physik, Bd. I, Springer-Verlag, Berlin, 1931. Zbl. 1, 5; English translation: Methods of mathematical physics, Vol. I, Interscience, New York 1953. Zbl. 53, 28

    Google Scholar 

  31. Dedekind, R., Weber, H.: Theorie der algebraischen Funktionen einer Veränderlichen, Crelle J. Reine Angew. Math. 92, 181–291 (1882). Jrb. 14, 352

    Google Scholar 

  32. Delone, B., Padurov, N., Aleksandrov, A.: The mathematical foundations of crystal structure analysis and the definition of the fundamental parallelipiped of repetition by X-ray diffraction, ONTI-GTTI, Moscow-Leningrad 1934 (in Russian)

    Google Scholar 

  33. Deuring, M.: Algebren, Springer-Verlag, Berlin 1935. Zbl. 11, 198

    Google Scholar 

  34. Dieudonné, J.A., Carrell, J.B.: Invariant theory, old and new, Academic Press, New York London 1971. Zbl. 258. 14011

    Google Scholar 

  35. Dirac, P.A.M.: The principles of quantum mechanics, Oxford Univ. Press, Oxford 1930. Jrb. 56, 745

    Google Scholar 

  36. Dold, A.: Lectures on algebraic topology, Grundlehren Math. Wiss. 200, Springer-Verlag, Berlin Heidelberg New York 1980. Zbl. 434. 55001

    Google Scholar 

  37. Dyson, F.J.: Mathematics in the physical sciences, Scientific American 211, 129–146 (1964)

    Article  MathSciNet  Google Scholar 

  38. Eilenberg, S., MacLane, S.: Natural isomorphisms in group theory, Proc. Natl. Acad. Sci. USA 28, 537–543 (1942). Zbl. 61, 92

    Google Scholar 

  39. Eilenberg, S., MacLane, S.: General theory of natural equivalence, Trans. Am. Math. Soc. 58, 231–294 (1945). Zbl. 61, 92

    Google Scholar 

  40. Fëdorov, E.S.: Symmetries in the plane, Zapiski imperatorskogo Sankt-Peterburgskogo mineralogicheskogo obshchestva (Notes of the imperial Saint Petersburg mineralogical society), 28 (2), 345–390 (1891) (in Russian). Jrb. 23, 539

    Google Scholar 

  41. Feynman, R.P.: The character of physical laws, Messenger Lectures, Cornell 1964, Cox and Wyman ( BBC publications ), London 1965

    Google Scholar 

  42. Fomenko, A.T.: Differential geometry and topology, Complementary chapters, Moscow Univ. publications, Moscow 1983 (in Russian). Zbl. 517. 53001

    Google Scholar 

  43. Freudenthal, H.: Octaven, Ausnahmegruppen und Octavengeometrien, Math. Inst. Rijksuniversitet Utrecht 1951. Zbl. 56, 259

    Google Scholar 

  44. Frobenius, G.: Gesammelte Abhandlungen, Bd. 1–3, Springer-Verlag, Berlin Heidelberg New York 1968. Zbl. 169, 289

    Google Scholar 

  45. Galois, E.: OEuvres mathématiques d’Évariste Galois, Gauthier-Villars, Paris 1951. Zbl. 42, 4

    Google Scholar 

  46. Gauss, C.F.: Disquisitiones arithmeticae, Werke, Bd. 1, Springer-Verlag, Berlin 1870; English translation: Yale, New Haven, Conn. London 1966. Zbl. 136, 323

    Google Scholar 

  47. Gel’fand, I.M., Raikov, D.A., Shilov, G.E.: Commutative normed rings, Fiz. Mat. G. Iz., Moscow 1960 Zbl. 134, 321; English translation: Chelsea, New York 1964

    Google Scholar 

  48. Goppa, V.D.: Codes and information, Usp. Mat. Nauk 39 No. 1, 77–120 (1984); English translation: Russ. Math. Surv. 39 No. 1, 87–141 (1984). Zbl. 578. 94011

    Google Scholar 

  49. Gorenstein, D.: Finite simple groups, An introduction to their classification, Univ. Series. in Math., Plenum Press New York, London 1982. Zbl. 483. 20008

    Google Scholar 

  50. Goto, M., Grosshans, F.D.: Semisimple Lie algebras, Lect. Notes. Pure Appl. Math. 38, Marcel Dekker, New York Basel 1978. Zbl. 391. 17004

    Google Scholar 

  51. Grothendieck, A.: Sur quelques points d’algèbre cohomologique, Tôhoku Math. J. II. Ser. 9, 119–221 (1957). Zbl. 118, 261

    Google Scholar 

  52. Grothendieck, A.: The cohomology theory of abstract algebraic varieties, Proc. Int. Congr. Math., Edinburgh 1958, Cambridge Univ. Press, Cambridge New York 1960, 103–118. Zbl. 119, 369

    Google Scholar 

  53. Grothendieck, A., Dieudonné, J.: Éléments de géométrie algébrique, III, Étude cohomologique des faisceaux cohérents, Publ. Math. Inst. Hautes Études Sci. 11 (1961), 1–167 (1962). Zbl. 118, 362

    Google Scholar 

  54. Hadamard, J.: Leçons de géométrie élémentaire, II, Géométrie dans l’espace, Armand Colin, Paris 1908

    Google Scholar 

  55. Hadamard, J.: Non-Euclidean geometry and the theory of automorphic functions, Gos. Izdat. Tekhn.-Teor. Lit., Moscow Leningrad 1951 (in Russian). Zbl. 45, 361

    Google Scholar 

  56. Hamermesh, M.: Group theory and its application to physical problems, Addison-Wesley, Reading, Mass. London 1964. Zbl. 151, 341

    Google Scholar 

  57. Hazewinkel, M.: Formal groups and applications, Pure Appl. Math. 78, Academic Press, New York London 1978. Zbl. 454. 14020

    Google Scholar 

  58. Hazewinkel, M., Hesselink, W., Siersma, D., Veldkamp, F.D.: The ubiquity of Coxeter-Dynkin diagrams (an introduction to the A-D-E problem), Nieuw Arch. Wisk. III. Ser. 25, 257–307 (1977). Zbl. 377. 20037

    Google Scholar 

  59. Hilbert, D.: Grundlagen der Geometrie, Teubner, Leipzig Berlin 1930. Jrb. 56, 481

    Google Scholar 

  60. Hilbert, D., Cohn-Vossen, S.: Anschauliche Geometrie, Springer-Verlag, Berlin 1932. Zbl. 5, 112; English translation: Geometry and the imagination, Chelsea, New York 1952. Zbl. 47, 388

    Google Scholar 

  61. Hilton, P.J., Stammbach, U.: A course in homological algebra, Grad. Texts Math. 4, Springer-Verlag, Berlin Heidelberg New York 1971. Zbl. 238. 18006

    Google Scholar 

  62. Hirzebruch, F.: Neue topologische Methoden in der algebraischen Geometrie, Springer-Verlag, Berlin Heidelberg New York 1956. Zbl. 70, 163; English translation: Topological methods in algebraic geometry, Springer-Verlag, Berlin Heidelberg New York 1966. Zbl. 138, 420

    Google Scholar 

  63. Hirzebruch, F.: Elliptische Differentialoperatoren auf Mannigfaltigkeiten, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen 33, 563–608 (1965). Zbl. 181, 103

    Google Scholar 

  64. Hochschild, G.: The structure of Lie groups, Holden-Day, San Francisco London Amsterdam 1965. Zbl. 131, 27

    Google Scholar 

  65. Hoffman, K.: Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, New Jersey 1962. Zbl. 117, 340

    Google Scholar 

  66. Humphreys, J.E.: Linear algebraic groups, Grad. Texts Math. 21, Springer-Verlag, Berlin Heidelberg New York 1975. Zbl. 325. 20039

    Google Scholar 

  67. Huppert, B.: Endliche Gruppen, Bd.I, Grundlehren Math. Wiss. 134, Springer-Verlag, Berlin Heidelberg New York 1967. Zbl. 217, 72

    Google Scholar 

  68. Huppert, B., Blackburn, N.: Finite groups, Vol. II—III, Springer-Verlag, Berlin Heidelberg New York 1982. II: Grundlehren Math. Wiss. 242. ZbI. 477.20001. III: Grundlehren Math. Wiss. 243. Zbl. 514. 20002

    Google Scholar 

  69. Ince, E.L.: Ordinary differential equations, Longmans-Green, London 1927. Jrb. 53, 399

    Google Scholar 

  70. Jordan, C.: Traité des substitutions des équations algébriques, Gauthier-Villars, Paris 1870

    Google Scholar 

  71. Kaplansky, I.: An introduction to differential algebra, Hermann, Paris 1957. Zbl. 83, 33

    Google Scholar 

  72. Kirillov, A.A.: Elements of the theory of representations, Nauka, Moscow 1972. Zbl. 264.22011; English translation: Grundlehren Math. Wiss. 220, Springer-Verlag, Berlin Heidelberg New York 1976. Zbl. 342. 22001

    Google Scholar 

  73. Klein, F.: Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, Grundlehren Math. Wiss. 24, Springer-Verlag, Berlin 1926. Jrb. 52, 22

    Google Scholar 

  74. Klemm, M.: Symmetrien von Ornamenten und Kristallen, Hochschultext, Springer-Verlag, Berlin Heidelberg New York 1982. Zbl. 482. 20034

    Google Scholar 

  75. Kostrikin, A.I., Manin, Yu.I.: Linear algebra and geometry, Moscow Univ. publications, Moscow 1980. Zbl. 532.00002; English translation: Gordon and Breach, New York London 1989

    Google Scholar 

  76. Kronecker, L.: Grundzüge einer arithmetischen Theorie der algebraischen Grössen, J. Reine Angew. Math. 92, 1–123 (1882). Jrb. 14, 38

    Google Scholar 

  77. Kurosh, A.G.: The theory of groups, Gos. Izdat. Teor.-Tekn. Lit., 1944; English translation: Vol. I, II, Chelsea, New York 1955, 1956. Zbl. 64, 251

    Google Scholar 

  78. Lawson, H.B. Jr.: Surfaces minimales et la construction de Calabi-Penrose, Séminaire Bourbaki, Exp. 624, Astérisque 121/122, 197–211 (1985)

    Google Scholar 

  79. Lie, S., Engel, F.: Theorie der Transformationsgruppen, Bd. I—III, Teubner, Leipzig, I 1883, II 1888, III 1893

    Google Scholar 

  80. Mal’tsev, A.I.: Groups and other algebraic systems, in Mathematics, its contents, methods and meaning, vol. 3, 248–331 Academy of Sciences of the USSR, Moscow 1956 (in Russian)

    Google Scholar 

  81. Manin, Yu.I.: A course in mathematical logic, Grad. Texts Math. 53, Springer-Verlag, Berlin Heidelberg New York 1977. Zbl. 383. 03002

    Google Scholar 

  82. Manin, Yu.I., Vlehduts, S.G.: Linear codes and modular curves, in Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 25, 209–257 (1984). Zbl. 629.94013; English translation: J. Soy. Math. 30, 2611–2643 (1985)

    Google Scholar 

  83. Manin, Yu.I.: Lectures on algebraic geometry, Part I, Affine schemes, Moscow Univ. publications, Moscow 1970 (in Russian)

    Google Scholar 

  84. Michel, L.: Symmetry defects and broken symmetry configurations, hidden symmetry, Rev. Mod. Phys. 52, 617–652 (1980)

    Article  Google Scholar 

  85. Milnor, J.: Introduction to algebraic K-theory, Ann. Math. Stud., Princeton Univ. Press, Princeton, New Jersey 1971. Zbl. 237. 18005

    Google Scholar 

  86. Mumford, D.: An algebro-geometric construction of commuting operators and of solutions to Toda lattice equations, Korteweg-de Vries equations and related non-linear equations, in Proc. int. symp. on algebraic geometry Kyoto 1977 Kinokuniya, Tokyo, 115–153, 1977, Zbl. 423. 14007

    Google Scholar 

  87. von Neumann, J.: Continuous geometry, Princeton Univ. Press, Princeton, New Jersey 1960. Zbl. 171, 280

    Google Scholar 

  88. Palais, R.S.: Seminar on the Atiyah-Singer index theorem, Ann. Math. Stud. 57, Princeton Univ. Press, Princeton, New Jersey 1965. Zbl. 137, 170

    Google Scholar 

  89. Pedersen, J.: Geometry: The unity of theory and practice, Math. Intell. 5 No. 4, 37–49, (1983), Zbl. 536.54008. B. Grünbaum, The Emperor’s new clothes: full regalia, G string, or nothing? Math. Intell. 6 No. 4, 47–53 (1984) Zbl. 561.52014, and P. Hilton and J. Pedersen, Comments on Grünbaum’s article, Math. Intelli. 6 No. 4, 54–56 (1984). Zbl. 561. 52015

    Google Scholar 

  90. Pontryagin, L.S.: Topological groups, Redak. tekh.-teor. lit., Moscow Leningrad 1938; English translation: Oxford Univ. Press, London Milford Haven Conn. Zbl. 22, 171

    Google Scholar 

  91. Quillen, D.: On the cohomology and K-theory of the general linear groups over a finite field, Ann. Math. (2) 96, 552–586 (1972). Zbl. 249. 18022

    Google Scholar 

  92. de Rham, G.: Variétés différentiables, Formes, courants, formes harmoniques, Hermann, Paris 1955. Zbl. 65, 324

    Google Scholar 

  93. Seifert, H., Threlfall, W.: Lehrbuch der Topologie, Teubner, Leipzig Berlin 1934. Zbl. 9, 86

    Google Scholar 

  94. Séminaire Sophus Lie,Théorie des algèbres de Lie, Topologie des groupes de Lie, Paris 1955

    Google Scholar 

  95. Serre, J-P.: Représentations linéaires des groupes finis, Hermann, Paris 1967; English translation: Linear representations of finite groups, Grad. Texts Math. 42, Springer-Verlag, Berlin Heidelberg New York 1977. Zbl. 355. 20006

    Google Scholar 

  96. Shafarevich, I.R.: Basic algebraic geometry, Nauka, Moscow 1972; English translation: Grundlehren Math. Wiss. 213, Springer-Verlag, Berlin Heidelberg New York 1974. Zbl. 284. 14001

    Google Scholar 

  97. Soulé, K.: K-théorie des anneaux d’entiers de corps de nombres et cohomologie étale, Invent. Math. 55, 251–295 (1979). Zbl. 437. 12008

    Google Scholar 

  98. Speiser, A.: Die Theorie der Gruppen von endlicher Ordnung, Springer-Verlag, Berlin 1937. Zbl. 17, 153

    Google Scholar 

  99. Springer, T.A.: Linear algebraic groups, Prog. Math. 9, Birkhäuser, Boston 1981. Zbl. 453. 14022

    Google Scholar 

  100. Suslin, A.A.: Algebraic K-theory and the norm residue homomorphism, in Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 25, 115–207 (1984). Zbl. 558.12013; English translation in J. Sov. Math. 30, 2556–2611 (1985)

    Google Scholar 

  101. Switzer, R.M.: Algebraic topology—homotopy and homology, Grundlehren Math. Wiss. 212, Springer-Verlag, Berlin Heidelberg New York 1975. Zbl. 305. 55001

    Google Scholar 

  102. Tennison, B.R.: Sheaf theory, Lond. Math. Soc. Lect. Notes 20, Cambridge Univ. Press, Cambridge New York 1975. Zbl. 313. 18010

    Google Scholar 

  103. Tits, J.: Groupes simples et géométries associées, in Proc. Int. Congr. Math., Stockholm, 1962, Inst. Mittag-Leffler, Djursholm 1963, 197–221. Zbl. 131, 265

    Google Scholar 

  104. van der Waerden, B.L.: Moderne Algebra, Bd. 1, 2, Springer-Verlag, Berlin 1930, 1931; I: Jrb. 56, 138. II: Zbl. 2, 8. English translation: Algebra, Vol. I, II, Ungar, New York 1970.

    Google Scholar 

  105. Weber, H.: Lehrbuch der Algebra, Bd. 1, 2, Vieweg, Braunschweig 1898, 1899

    Google Scholar 

  106. Weil, A.: Basic number theory, Grundlehren Math. Wiss. 144, Springer-Verlag, Berlin Heidelberg New York 1967. Zbl. 176, 336

    Google Scholar 

  107. Weyl, H.: Gruppentheorie und Quantenmechanik, Hirzel, Leipzig 1928; English translation: The theory of groups and quantum mechanics, Princeton 1930. Jrb. 54, 954

    Google Scholar 

  108. Weyl, H.: Mathematische Analyse des Raumproblems, Springer-Verlag, Berlin 1923. Jrb. 49, 81. Reprinted Wissenschaftliche Buchgesellschaft, Darmstadt 1977

    Google Scholar 

  109. Weyl, H.: The classical groups, Princeton Univ. Press, Princeton, New Jersey 1939. Zbl. 20, 206

    Google Scholar 

  110. Weyl, H.: Symmetry, Princeton Univ. Press, Princeton, New Jersey, 1952. Zbl. 46, 4

    Google Scholar 

  111. Zhelobenko, D.P.: Compact Lie groups and their representations, Nauka, Moscow 1970; English translation: Am. Math. Soc., Providence 1973. Zbl. 228. 22013

    Google Scholar 

Added in translation

  1. Cohn, P.M.: Algebra, vol. 1, 2, J. Wiley, London New York Sidney 1974, 1977. 1: Zbl. 272.00003. 2: Zbl. 341.00002, 2nd ed.: J. Wiley, 1982, Zbl. 481. 00001

    Google Scholar 

  2. Curtis, C.W., Reiner, I.: Methods of representation theory, vol. I, II, Pure and Applied Mathematics, J. Wiley, London New York Sidney 1981, 1987. I: Zbl. 469.20001. II: Zbl. 616. 20001

    Google Scholar 

  3. Jacobson, N.: Lectures in abstract algebra, vol. I, II, III, Van Nostrand, Princeton, New Jersey 1951, 1953, 1964, I: Zbl, 44, 260. II: Zbl. 53, 212. III: Zbl. 124, 270

    Google Scholar 

  4. Matsumura, H.: Commutative ring theory, C.U.P, Cambridge New York Melbourne, 1986. Translation from the Japanese (Kyoritsu Tokyo 1980) Zbl. 603. 13001

    Google Scholar 

Download references

Authors
  1. I. R. Shafarevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, ul. Vavilova 42, 117966, Moscow, USSR

    A. I. Kostrikin  & I. R. Shafarevich  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Shafarevich, I.R. (1990). Basic Notions of Algebra. In: Kostrikin, A.I., Shafarevich, I.R. (eds) Algebra I. Encyclopaedia of Mathematical Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39643-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-39643-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-38753-5

  • Online ISBN: 978-3-662-39643-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation