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Generalized semigroup rings

  • Partially Ordered Algebraic Structures
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Algebra Carbondale 1980

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 848))

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References

  1. C. G. Chehata, "On an ordered semigroup", Jour. London Math. Soc. 28(1953), 353–356. (MR 14 #944)

    Article  MathSciNet  MATH  Google Scholar 

  2. P. M. Cohn, Skew Field Constructions, Cambridge University Press 1977.

    Google Scholar 

  3. P. Conrad, "On ordered division rings", Proc. Amer. Math. Soc. (1954), 323–328. (MR 15 #849)

    Google Scholar 

  4. P. Conrad, "Ordered semigroups", Nagoya Math. Jour. 16(1960), 51–64. (MR 22 #735)

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Conrad, "Generalized semigroup rings", Jour. Indian Math. Soc. 21(1957), 73–95. (MR 20 #887)

    MathSciNet  MATH  Google Scholar 

  6. P. Conrad, "Generalized semigroup rings II", Portugaliae Mathematica 18(1959), 33–52. (MR 22 #4752)

    MathSciNet  MATH  Google Scholar 

  7. P. Conrad and P. McCarthy, "The structure of f-algebras", Mathem. Nachrichten 58(1973), 169–191. (MR 48 #8339)

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Conrad and J. Dauns, "An embedding theorem for lattice ordered fields", Pac. J. Math. 30(1969), 385–398. (MR 40 #128)

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Croisot, "Automorphismes intérieurs dún semi-groupe", Bull. Soc. Math. France 82(1954), 161–193. (MR 16 #215)

    MathSciNet  MATH  Google Scholar 

  10. J. Dauns, "Integral domains that are not embeddable in division rings", Pac. J. Math. 34(1970), 27–31. (MR 43 #4744)

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Dauns, "Semigroup power series rings", Pac. J. Math 34(1970), 365–369. (MR 42 #4464)

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Dauns, "Embeddings in division rings", Trans. Amer. Math. Soc. 150(1970), 287–299. (MR 41 #6901)

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Dauns, "Ordered domains", Symposia Mathematicae XXI (1977), 565–587.

    MathSciNet  MATH  Google Scholar 

  14. J. Dauns, "Noncyclic division rings", Math. Zeitsch. 169(1979), 195–204.

    Article  MathSciNet  MATH  Google Scholar 

  15. L. Fuchs, "On the ordering of quotient rings and quotient semigroups", Acta Sci. Math. Szeged 22(1961), 42–45. (MR 23 #A2445)

    MathSciNet  MATH  Google Scholar 

  16. L. Fuchs, Partially Ordered Algebraic Systems, Pergammon Press, Addison-Wesley, Reading, Mass., 1963. (MR 30 #2090)

    MATH  Google Scholar 

  17. L. Fuchs, Teilweise geordnete algebraische Strukturen, Akadémiai Kiado-Budapest, 1966. (MR 34 #4386)

    Google Scholar 

  18. J. Hannah, "Simple quotient rings of group algebras", J. Alg. 59(1979), 188–201.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Hannah, "Ideals in regular self-injective rings and quotient rings of group algebras", Proc. London Math. Soc., to appear.

    Google Scholar 

  20. C. Holland, "A totally ordered integral domain with a convex left ideal which is not an ideal", Proc. Amer. Math. Soc. 11(1960), 703. (MR 23 #A2446)

    Article  MathSciNet  MATH  Google Scholar 

  21. R. Irving, "Some primitive group rings", J. Alg. 56 (1979), 274–281.

    Article  MathSciNet  MATH  Google Scholar 

  22. R. Irving, "On the primitivity of certain Ore extensions", Math. Ann. 272(1979), 177–192.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Irving, "Prime ideals of Ore extensions over commutative rings, II", J. Alg. 58(1979), 399–423.

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Irving, "Some more primitive group rings", to appear.

    Google Scholar 

  25. A. V. Jategaonkar, "Left principal ideal domains", Jour. Alg. 8, (1968), 148–155. (MR 36 # 1474)

    Article  MathSciNet  MATH  Google Scholar 

  26. A. V. Jategaonkar, Left principal ideal domains, Springer, Lecture Notes in Mathematics, No. 123, Berlin-New York, 1969. (MR 41 #8449)

    Google Scholar 

  27. N. Jacobson, The Theory of Rings, Math. Surveys II, Amer. Math. Soc. 21(1969), 211–213.

    Google Scholar 

  28. R. E. Johnson, "Extended Malcev domains", Proc. Amer. Math. Soc. 21(1969), 211–213. (MR 38 #5957)

    Article  MathSciNet  MATH  Google Scholar 

  29. R. E. Johnson, "Unique factorization monoids and domains", Proc. Amer. Math. Soc. 28(1971), 397–404. (MR 43 #3186)

    Article  MathSciNet  MATH  Google Scholar 

  30. D. A. Jordan, "Primitive skew Laurent polynomial rings", Glasgow Math. J. 19(1978), 79–85.

    Article  MathSciNet  MATH  Google Scholar 

  31. A. I. Malcev, "On embedding of group algebra in a division ring", Dokl. Akad. Nauk. S.S. S.R. 60(1948), 1499–1501. (MR 10 #8)

    MathSciNet  Google Scholar 

  32. C. McGregor, "On the prmitivity of the group ring of a free group", Bull. London Math. Soc. 8(1976), 294–298. (MR 54 #7530)

    Article  MathSciNet  MATH  Google Scholar 

  33. S. Montgomery and D. S. Passman, "Crossed products over prime rings", to appear.

    Google Scholar 

  34. B. H. Neumann, "On ordered division rings", Trans. Amer. Math. Soc. 66(1949), 202–252. (MR 11 #311)

    Article  MathSciNet  MATH  Google Scholar 

  35. D. S. Passman, Algebraic Structure of Group Rings, Wiley-Interscience, New York, 1977. (MR 11 #311)

    MATH  Google Scholar 

  36. W. Powell, "Projectives in a class of lattice ordered modules", Alg. Univ., to appear.

    Google Scholar 

  37. S. Steinberg, "An embedding theorem for commutative lattice—ordered domains", Proc. Amer. Math. Soc. 31(1972), 409–416. (MR 44 #2682)

    Article  MathSciNet  MATH  Google Scholar 

  38. M. Satyanarayana, "Principal right ideal semigroups", J. London Math. Soc. 2(1971), 549–553. (MR 44 #348)

    Article  MathSciNet  MATH  Google Scholar 

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Ralph K. Amayo

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© 1981 Springer-Verlag

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Dauns, J. (1981). Generalized semigroup rings. In: Amayo, R.K. (eds) Algebra Carbondale 1980. Lecture Notes in Mathematics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090570

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  • DOI: https://doi.org/10.1007/BFb0090570

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  • Print ISBN: 978-3-540-10573-2

  • Online ISBN: 978-3-540-38549-3

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