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Algebras and relational structures

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Topics in Universal Algebra

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References to Section 2.3

  1. S. D. Comer and J. J. LeTourneau, "Isomorphism types of infinite algebras", Proc. Amer. Math. Soc. 21(1969), 635–639.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. L. Davis, "The number of structures of finite relations", Proc. Amer. Math. Soc. 4(1953), 486–495.

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Fuchs, "Abelian Groups", New York: 1960.

    Google Scholar 

  4. M. A. Harrison, "Note on the number of finite algebras", J. Combinatorial Theory 1(1966), 395–397.

    Article  MathSciNet  MATH  Google Scholar 

  5. L. Ya. Kulikov, "Generalized primary groups, II", Trudy Moskov. Mat. Obšč. 2(1953), 85–167. (Russian).

    MathSciNet  Google Scholar 

  6. A. G. Kurosh, "Some remarks on the theory of infinite groups", Mat. Sbornik 5(1939), 347–354. (Russian).

    Google Scholar 

References for Section 2.4

  1. M. Armbrust and J. Schmidt, "Zum Cayleyschen Darstellungssatz", Mathematische Annalen 154(1964), 70–73.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Jónsson, "Algebraic structures with prescribed automorphism groups", Coll. Math. 19(1968), 1–4.

    MathSciNet  MATH  Google Scholar 

  3. M. Krasner, "Generalisation abstraite de la théorie de Galois", Algèbre et Théorie des Nombres. Colloques Internationaux de Centre National de la Recherche Scientifique no. 24, pp. 163–168. Centre National de la Recherche Scientifique, Paris 1950.

    Google Scholar 

  4. E. Plonka, "A problem of B. Jónsson concerning automorphisms of a general algebra", Coll. Math. 19(1968), 5–8.

    MathSciNet  MATH  Google Scholar 

Bibliography for Sections 2.5,–2.7

  1. M. Allen, "Representations of semigroups by endomorphisms", M.A. thesis, Vanderbilt University, 1969.

    Google Scholar 

  2. G. Birkhoff, "On groups of automorphisms" (Spanish), Revista Union Math. Argentina 11(1946), 155–157; MR7, p. 411.

    MathSciNet  Google Scholar 

  3. V. Chvátal, "On finite and countable rigid graphs and tournaments", Comm. Math. Univ. Carolinae 6(1965), 429–438.

    MathSciNet  MATH  Google Scholar 

  4. B. Csahany, "Inner automorphisms of universal algebras", Publ. Math. Debrecen 12(1965), 331–333; MR13, #2356.

    MathSciNet  Google Scholar 

  5. A. Daigneault, "On automorphisms of polyadic algebras", Trans. Amer. Math. Soc. 112(1964), 84–130; MR29, #45.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Dlab and B. H. Neumann, "Semigroups with few endomorphisms", Australian J. of Math., Vol. 10 (1969), 162–168.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Ehrenfeucht, "Models of axiomatic theories admitting automorphisms", Fund. Math. 43(1956), 50–68; MR18, #863.

    MathSciNet  MATH  Google Scholar 

  8. —, "Elementary theories with models without automorphisms", Proc. 1963 Int. Symp. at Berkeley, North-Holland, Amsterdam, 1965, 70–76.

    Google Scholar 

  9. A. L. Foster, "Automorphisms and functional completeness in universal algebra I. General automorphisms, structure theory and characterization", Math. Ann. 180(1969), 138–169.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Frucht, "Graphs of degree three with a given abstract group", Canad. J. Math. 1(1949), 365–378; MR11, p. 377.

    Article  MathSciNet  MATH  Google Scholar 

  11. —, "Herstellung von Graphen mit vorgegebener abstrakter Gruppe", Compos. Math. 6(1938), 239–250.

    MathSciNet  MATH  Google Scholar 

  12. —, "Lattices with a given abstract group of automorphisms", Canad. J. Math. 2(1950), 417–419; MR12, p. 473.

    Article  MathSciNet  MATH  Google Scholar 

  13. —, "On the construction of partially ordered sets with given automorphism groups" (Spanish), Revista Union Math. Argentina 13(1948), 12–18.

    MathSciNet  Google Scholar 

  14. —, "On the construction of partially ordered systems with a given group of automorphisms", Amer. Math. J. 72(1950), 195–199; MR11, p. 320.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Fuhrken, "On automorphisms of algebras with a single unary operator", mimeographed note.

    Google Scholar 

  16. G. Grätzer, "On the endomorphism semigroup of simple algebras", Math. Ann. 170(1967), 334–338.

    Article  MathSciNet  MATH  Google Scholar 

  17. Z. Hedrlin, "On endomorphisms of graphs and their homomorphic images", to appear in Proof Techniques in Graph Theory.

    Google Scholar 

  18. Z. Hedrlin and J. Lambek, "How comprehensive is the category of semigroups?", J. of Algebra 11(1969), 195–212.

    Article  MathSciNet  MATH  Google Scholar 

  19. Z. Hedrlin and R. H. McDowell, "Partly ordered sets with given monoid of order preserving maps", to appear.

    Google Scholar 

  20. Z. Hedrlin and E. Mendelsohn, "On the category of graphs with a given subgraph. Applications to topology and algebra", to appear in Can. J. Math.

    Google Scholar 

  21. Z. Hedrlin and A. Pultr, "On full embeddings of categories of algebras", Ill. J. of Math. 10(1966), 392–406.

    MathSciNet  MATH  Google Scholar 

  22. —, —, "On rigid undirected graphs", Canad. J. Math., 18(1966), 1237–1242.

    Article  MathSciNet  MATH  Google Scholar 

  23. —, —, "Relations (graphs) with given finitely generated semigroups", Monatsheft für Math. 68(1964), 213–217.

    Article  MathSciNet  MATH  Google Scholar 

  24. —, —, "Symmetric relations (undirected graphs) with given semigroups", Monatsheft für Math. 69(1965), 318–322.

    Article  MathSciNet  MATH  Google Scholar 

  25. Z. Hedrlin, A. Pultr and V. Trnková, "Concerning a categorical approach to topological and algebraic theories", Proc. of the Second Prague Topological Symposium 1966, Praha 1967, 176–181.

    Google Scholar 

  26. J. Johnson and R. L. Seifert, "A survey of multiunary algebras", Dittoed seminar notes, U.C. Berkeley, 1967, 27 pages.

    Google Scholar 

  27. B. Jónsson, "A Boolean algebra without proper automorphisms", Proc. Amer. Math. Soc. 68(1951), 766–770.

    Article  MathSciNet  MATH  Google Scholar 

  28. E. Mendelsohn, "Full embeddings and the category of graphs with applications to topology and algebra", Thesis, McGill University, 1968.

    Google Scholar 

  29. —, Šip-indikátors, products, and graphs with given semigroups", Mimeographed notes (undated), 30 pages.

    Google Scholar 

  30. C. Platt, "A note on endomorphism semigroups", Mimeographed notes, 1968, 4 pages.

    Google Scholar 

  31. B. I. Plotkin, "The automorphism groups of algebraic systems" (Russian), Izd. Nauka, Moscow, 1966, 603 pages.

    Google Scholar 

  32. A. Pultr, "Concerning universal categories", Comm. Math. Univ. Carolinae, 5(1964), 227–239.

    MathSciNet  MATH  Google Scholar 

  33. —, "Eine Bemerkung über volle Einbettungen von Kategorien von Algebren", Math. Ann., 178(1968), 78–82.

    Article  MathSciNet  MATH  Google Scholar 

  34. —, "On full embeddings of concrete categories with respect to forgetful functors", Comm. Math. Univ. Carolinae, 9(1968), 281–305.

    MathSciNet  MATH  Google Scholar 

  35. A. Pultr and Z. Hedrlin, "Relations (graphs) with given infinite semigroups", Monatshefte für Math. 68(1964), 421–425.

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Pultr and J. Sichler, "Primitive classes of algebras with two unary idempotent operations, containing all algebraic categories as full subcategories", Mimeographed notes (undated), 22 pages.

    Google Scholar 

  37. M. O. Rabin, "Universal groups of automorphisms of models", The Theory of Models, Proc. 1963 International Symposium at Berkeley, North-Holland, Amsterdam, 1965, 274–284, MR34, #1191.

    Google Scholar 

  38. L. Rieger, "Some remarks on automorphisms of Boolean algebras", Fund. Math. 38(1951), 209–216.

    MathSciNet  MATH  Google Scholar 

  39. G. Sabbidussi, "Graphs with given group and given graphtheoretic properties", Can. J. Math. 9(1958), 515–525.

    Article  Google Scholar 

  40. —, "On the minimum order of graphs with given automorphism groups", Monatshefte für Math. 63(1959), 124–127.

    Article  Google Scholar 

  41. E. T. Schmidt, "Universale Algebren mit gegebenen Automorphismen Gruppen und Unteralgebraverbanden", Acta Sci. Math. (Szeged) 24(1963), 251–254; MR28, #2987.

    MathSciNet  MATH  Google Scholar 

  42. —, "Universale Algebren mit gegebenen Automorphismen Gruppen und Kongruenzverbanden", Acta Math. Acad. Sci. Hungar, 15(1964), 37–45; MR29, #3411.

    Article  MathSciNet  MATH  Google Scholar 

  43. J. Sichler, "00(1,1) can be strongly embedded in category of semigroups", Comm. Math. Univ. Carolinae 9(1968), 257–262.

    MathSciNet  MATH  Google Scholar 

  44. —, "Category of commutative groupoids is binding", Comm. Math. Univ. Carolinae 8(1967), 753–755.

    MathSciNet  MATH  Google Scholar 

  45. —, "Concerning automorphisms of finite algebras", Comm. Math. Univ. Carolinae 8(1967).

    Google Scholar 

  46. —, "Concerning minimal primitive classes of algebras containing any category of algebras as a full subcategory", Comm. Math. Univ. Carolinae 9(1968), 627–635.

    MathSciNet  MATH  Google Scholar 

  47. —, "Rich small categories", to appear.

    Google Scholar 

  48. V. Trnková, "Strong embedding of category of all groupoids into category of semigroups", Comm. Math. Univ. Carolinae 9(1968), 251–256.

    MathSciNet  MATH  Google Scholar 

  49. P. Vopěnka, A. Pultr and Z. Hedrlin, "A rigid relation exists on any set", Comm. Math. Univ. Carolinae 6(1965), 149–155.

    MathSciNet  MATH  Google Scholar 

  50. H. deVries and A. B. deMiranda, "Groups with a small number of automorphisms", Math. Zeitschr. 68(1958), 450–464.

    Article  MathSciNet  Google Scholar 

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Jónsson, B. (1972). Algebras and relational structures. In: Topics in Universal Algebra. Lecture Notes in Mathematics, vol 250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058650

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  • DOI: https://doi.org/10.1007/BFb0058650

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