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The fine spectrum of a variety

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References

  1. A. I. Abakumov, F. A. Palyutin, M. A. Taîtslin, and Yu. E. Shishmarev,Categorical quasivarieties, Algebra i Logika11 (1972), 3–38.

    MATH  MathSciNet  Google Scholar 

  2. I. Sh. Aliev,On the minimal variety of a symmetric algebra, Algebra i Logika5 (#6) (1966), 5–14.

    MATH  MathSciNet  Google Scholar 

  3. A. K. Austin,A note on models of identities, Proc. Amer. Math. Soc.16 (1965), 522–523.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. T. Baldwin, and A. H. Lachlan,On strongly minimal sets, J. Symbolic Logic36 (1971), 79–96.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. T. Baldwin and A. H. Lachlan,On universal Horn classes categorical in some infinite power, Algebra Universalis3 (1973), 98–111.

    MATH  MathSciNet  Google Scholar 

  6. B. Banaschewski,Equational compactness of G-sets, Canad. Math. Bull,17 (1974), 11–18.

    MATH  MathSciNet  Google Scholar 

  7. B. Banaschewski and E. Nelson,Varieties of squags (to appear).

  8. J. H. Bennett,On spectra, Ph. D. Thesis, Princeton, 1962 Abstract:J. Symbolic Logic 30 (1965), 264.

  9. C. Bernardi,Su alcuni condizioni necessarie per l'indipendenza di due varietà di algebre, Boll. Un. Mat. Ital. (4)6 (1972), 410–421.

    MATH  MathSciNet  Google Scholar 

  10. G. Birkhoff,Lattice theory, Amer Math. Soc. Colloq. Publ. #25, 3rd Ed., Providence, 1967.

  11. S. N. Burris,Models in equational theories of unary algebras, Algebra Universalis1 (1971), 386–392.

    MathSciNet  Google Scholar 

  12. S. Burris,Boolean powers, mimeographed, Waterloo, 1974.

  13. C. C. Chang, B. Jónsson, and A. Tarski,Refinement properties for relational structures, Fund. Math.55 (1964), 249–281.

    MATH  MathSciNet  Google Scholar 

  14. L. M. Chawla and J. E. Maxfield,On the classification and evaluation of some partition functions and their tables, 103–112 in: Lecture Notes in Mathematics #251, Springer-Verlag, Berlin, 1972.

    Google Scholar 

  15. A. H. Clifford and G. B. Preston,The algebraic theory of semigroups, Vol. I, Amer. Math. Soc. Math. Surveys #7 (1971).

  16. H. Draškovičová,Independence of equational classes, Mat. Časopis, Slovensk. Acad. Vied23 (1973), 125–135.

    MATH  Google Scholar 

  17. R. B. Eggleton,Number of non-isomorphic groups of a given order, Advanced problem #5838, Amer. Math. Monthly80 (1973), 445–446.

    Article  MathSciNet  Google Scholar 

  18. T. Evans,Products of points—some simple algebras and their identities, Amer. Math. Monthly74 (1967), 362–372.

    Article  MATH  MathSciNet  Google Scholar 

  19. T. Evans,The spectrum of a variety, Z. Math. Logik u. Grundlagen der Math.13 (1967), 213–218.

    MATH  Google Scholar 

  20. S. Fajtlowicz,Birkhoff's theorem in the category of non-indexed algebras, Bull. Acad. Polon. Sci., Sér. Sci. Math. Phys. et Astron.17 (1969), 273–275.

    MATH  MathSciNet  Google Scholar 

  21. S. Fajtlowicz,n-Dimensional dice, Rend. Mat. (6)4 (1971), 1–11.

    MathSciNet  Google Scholar 

  22. S. Fajtlowicz,Categoricity in varieties, Abstract 72T-A109, Notices Amer. Math. Soc.19 (1973), A-435.

    Google Scholar 

  23. G. E. Forsythe,SWAC computes 126 distinct semigroups of order 4, Proc. Amer. Math. Soc.6 (1955), 443–447.

    Article  MathSciNet  Google Scholar 

  24. A. L. Foster and A. F. Pixley,Algebraic and equational seminaximality; equational spectra. II., Math. Z.94 (1966), 122–133.

    Article  MATH  MathSciNet  Google Scholar 

  25. P. Freyd,Abelian categories, Harper and Row, New York, 1964.

    MATH  Google Scholar 

  26. E. Fried and G. Grätzer,A nonassociative extension of the class of distributive lattices, Pacific J. Math.49 (1973), 59–78.

    MATH  MathSciNet  Google Scholar 

  27. O. Frink,The operations of Boolean algebras, Annals of Math (2)27 (1925), 477–490.

    MathSciNet  Google Scholar 

  28. J. Froemke and R. W. Quackenbush,The spectrum of an equational class of groupoids, Abstract 74T-A115, Notices Amer. Math. Soc.21 (1974), A-432.

    Google Scholar 

  29. P. X. Gallagher,Counting finite groups of a given order, Math. Z.102 (1967), 236–237.

    Article  MATH  MathSciNet  Google Scholar 

  30. S. Givant,Ph.D. Thesis, Berkeley, 1974.

  31. A. Goetz,A generalization of the notion of direct product of universal algebras, Colloq. Math.22 (1971), 167–176.

    MATH  MathSciNet  Google Scholar 

  32. G. Grätzer,On spectra of classes of universal algebras, Proc. Amer. Math. Soc.18 (1967), 729–735.

    Article  MATH  MathSciNet  Google Scholar 

  33. G. Grätzer,Universal algebra, van Nostrand, Princeton, 1968.

    MATH  Google Scholar 

  34. G. Grätzer,Composition of functions, Proceedings of the conference on Universal Algebra (October, 1969), Queen's Papers in Pure and Applied Mathematics #25, Kingston, Ontario, 1970, 1–106.

  35. G. Grätzer,Two Mal'cev-type theorems in universal algebra, J. Combinatorial Theory8 (1970), 334–342.

    MATH  MathSciNet  Google Scholar 

  36. G. Grätzer, H. Lakser, and J. Pŀonka,Joins and direct products of equational classes, Canad. Math. Bull.12 (1969), 741–744.

    MATH  MathSciNet  Google Scholar 

  37. G. Grätzer and R. McKenzie,Equational spectra and reduction of identities (abstract), Notices Amer. Math. Soc.14 (1967), 697.

    Google Scholar 

  38. A. A. Grau,Ternary Boolean algebra, Bull. Amer. Math. Soc.53 (1947), 567–572.

    MATH  MathSciNet  Google Scholar 

  39. A. A. Grau,A ternary operation related to the complete disjunction of Boolean algebra, Univ. Nac. Tucumán Rev. Ser. A8 (1951).

  40. G. Higman,Enumerating p-groups I, Inequalities Proc. London Math. Soc. (3)10 (1960), 24–30.

    MATH  MathSciNet  Google Scholar 

  41. T.-K. Hu and P. Kelenson,Independence and direct factorization of universal algebras, Math. Nachr.51 (1971), 83–99.

    MATH  MathSciNet  Google Scholar 

  42. A. Hulanicki, and S. Świerczkowski,Number of algebras with a given set of elements, Bull. Acad. Sci. Polon., Sér. Sci. Math. Phys. et Astron.8 (1960), 283–284.

    MATH  Google Scholar 

  43. B. Jónsson,The unique factorization problem for finite relational structures, Colloq. Math.14 (1966), 1–32.

    MATH  MathSciNet  Google Scholar 

  44. B. Jónsson,Algebras whose congruence lattices are distributive, Math. Scand.21 (1967), 110–121.

    MATH  MathSciNet  Google Scholar 

  45. B. Jónsson and E. Nelson,Regular varieties Alg. Univ.4 (1974), 14–19.

    MATH  Google Scholar 

  46. A. B. Kempe,On the relation between the logical theory of classes and the geometrical theory of points, Proc. London Math. Soc.(1)21 (1890), 147–182.

    MATH  Google Scholar 

  47. D. E. Knuth,Notes on central groupoids, J. Combinatorial Theory8 (1970), 376–390.

    MATH  MathSciNet  Google Scholar 

  48. J. D. Leech, (ed.),Computational problems in abstract algebra (Proceedings of a Conference at Oxford, 1967), Pergamon, Oxford, 1970.

    MATH  Google Scholar 

  49. C. C. Lindner,On the construction of non-isomorphic Steiner quadruple systems, Colloq. Math.29 (1974), 303–306.

    MATH  MathSciNet  Google Scholar 

  50. L. Lovász,Operations with structures, Acta Math. Acad. Sci. Hung.18 (1967), 321–328.

    Article  MATH  Google Scholar 

  51. L. Lovász,On the cancellation law among finite structures, Periodica Math. Hung.1 (1971), 145–156.

    Article  MATH  Google Scholar 

  52. R. C. Lyndon,Identities in two-valued calculi, Trans. Amer. Math. Soc.71 (1951). 457–465.

    Article  MATH  MathSciNet  Google Scholar 

  53. E. Marczewski,Independence in abstract algebras, results and problems, Colloq. Math.14 (1966), 169–188.

    MATH  MathSciNet  Google Scholar 

  54. N. H. McCoy,Rings and ideals, Carus monograph #8, Mathematical Association of America, 1948.

  55. N. H. McCoy and D. Montgomery,A representation of generalized Boolean rings, Duke Math. J.3 (1937), 455–459.

    Article  MATH  MathSciNet  Google Scholar 

  56. R. McKenzie,On the unique factorization problem for finite commutative semigroups, Notices Amer. Math. Soc.12 (1965), 315.

    Google Scholar 

  57. R. McKenzie,A method for obtaining refinement theorems with an application to direct products of semigroups, Algebra Universalis2 (1972), 324–338.

    MATH  MathSciNet  Google Scholar 

  58. R. McKenzie,On spectra and the negative solution of the decision problem for identies having a finite model, J. Symbolic Logic40 (1975), 186–196.

    Article  MATH  MathSciNet  Google Scholar 

  59. G. McNulty and R. W. Quackenbush,The ascending and descending varietal chains of a variety, Abstract 73T-A52, Notices Amer. Math. Soc.20 (1973), A-254. See also [98]B. Jónsson, G. McNulty, and R. Quackenbush,The ascending and descending variental chains of a variety, Canad. J. Math.27 (1975), 25–31.

    Google Scholar 

  60. N. S. Mendelsohn and R. Padmanabhan,A single identity for Boolean groups and Boolean rings, J. Algebra20 (1972), 78–82.

    Article  MATH  MathSciNet  Google Scholar 

  61. J. D. Monk,Some cardinal functions on algebras, Algebra Universalis5 (1975), 76–81.

    MATH  MathSciNet  Google Scholar 

  62. J. D. Monk and F. M. Sioson,On the general theory of m-groups, Fund. Math.72 (1971), 233–244.

    MATH  MathSciNet  Google Scholar 

  63. M. D. Morley,Categoricity in power, Trans. Amer. Math. Soc.114 (1965), 514–538.

    Article  MATH  MathSciNet  Google Scholar 

  64. B. H. Neumann,On a problem of G. Grätzer, Publ. Math. Debrecen14 (1967), 325–329.

    MATH  MathSciNet  Google Scholar 

  65. W. D. Neumann,Representing varieties of algebras by algebras, J. Austral. Math. Soc.11 (1970), 1–8.

    Article  MATH  MathSciNet  Google Scholar 

  66. M. H. A. Newman,A characterization of Boolean lattices and rings, J. London Math. Soc.16 (1941), 256–272.

    MATH  MathSciNet  Google Scholar 

  67. E. A. Palyutin,Models with countably categorical universal theories, Algebra i Logika10 (1971), 23–32.

    MATH  MathSciNet  Google Scholar 

  68. D. Pigozzi,The join of equational theories, Colloq. Math.30 (1974), 15–25.

    MATH  MathSciNet  Google Scholar 

  69. A. F. Pixley,Functionally complete algebras generating distributive and permutable classes, Math. Z.114 (1970), 361–372.

    Article  MathSciNet  Google Scholar 

  70. A. F. Pixley,The ternary discriminator function in universal algebra, Math. Ann.191 (1971), 167–180.

    Article  MATH  MathSciNet  Google Scholar 

  71. A. F. Pixley,Completeness in arithmetical algebras, Algebra Universalis2 (1972), 179–196.

    MATH  MathSciNet  Google Scholar 

  72. R. J. Plemmons,Construction and analysis of non-equivalent finite semigroups, 223–228 in Leech [48].

    Google Scholar 

  73. J. Pŀonka,Diagonal algebras, Fund. Math.58 (1966), 309–321.

    MathSciNet  MATH  Google Scholar 

  74. J. Pŀonka,On algebras with [at most] n distinct eessentially n-ary operations, Algebra Universalis1 (1971), 73–79 and 80–85.

    MathSciNet  MATH  Google Scholar 

  75. E. Post,Polyadic groups, Trans. Amer. Math. Soc.48 (1940), 208–350.

    Article  MATH  MathSciNet  Google Scholar 

  76. E. Post,The two-valued iterative systems of mathematical logic, Annals of Mathematics Studies #5, Princeton University Press, Princeton, 1941.

    MATH  Google Scholar 

  77. R. W. Quackenbush,Structural theory for equational classes generated by quasi-primal algebras, Trans. Amer. Math. Soc.187 (1974), 127–145.

    Article  MATH  MathSciNet  Google Scholar 

  78. D. Rearick,Operators on algebras of arithmetic functions, Duke Math. J.35 (1968), 761–766.

    Article  MATH  MathSciNet  Google Scholar 

  79. B. Rokowska,On the number of non-isomorphic Steiner triples, Colloq. Math.27 (1973), 149–160.

    MATH  MathSciNet  Google Scholar 

  80. P. C. Rosenbloom,Post algebras I, postulates and general theory, Amer J. Math.64 (1942), 167–188.

    Article  MATH  MathSciNet  Google Scholar 

  81. M. Saade,A comment on a paper by Evans, Z. Math. Logik u. Grundlagen der Math.15 (1969), 97–100.

    MATH  MathSciNet  Google Scholar 

  82. H. Scholz,Problem #1, J. Symbolic Logic17 (1952), 160.

    Google Scholar 

  83. L. E. Shader,On the existence of finite central groupoids of all possible ranks. I, J. Combinatorial Theory (A)16 (1974), 221–229.

    Article  MATH  MathSciNet  Google Scholar 

  84. S. Shelah,Stability, etc., Ann. Math. Logic3 (1971), 271–362.

    Article  MATH  MathSciNet  Google Scholar 

  85. C. C. Sims,Enumerating p-groups, Proc. London Math. Soc. (3),15 (1965), 151–166.

    MATH  MathSciNet  Google Scholar 

  86. D. M. Smirnov,Cantor algebras with a single generator I, II, Algebra i Logika10 (1971), 61–75 and 658–667.

    MATH  MathSciNet  Google Scholar 

  87. T. Tamura,Some contributions of computation to semigroups and groupoids, 229–261 in Leech [48].

    Google Scholar 

  88. W. Taylor,The fine spectrum of a variety, Abstract 72T-A250, Notices Amer. Math. Soc.19 (1972), A-686.

    Google Scholar 

  89. W. Taylor,Characterizing Mal'cev conditions, Algebra Universalis3 (1973), 351–397.

    Article  MATH  MathSciNet  Google Scholar 

  90. R. L. Vaught,Denumerable models of complete theories, 303–321 in:Infinitistic methods (Proceedings of the Symposium on Foundations of Mathematics. Warsaw, September, 1959), Pergamon Państwowe Wydawnictwo Naukowe, Warsaw, 1961.

    Google Scholar 

  91. H. Werner,Eine Charakterisierung funktional vollständiger Algebren, Arch. Math. (Basel)21 (1970), 381–385.

    MATH  MathSciNet  Google Scholar 

  92. A. Whiteman,Postulates for Boolean algebra in terms of ternary rejection, Bull. Amer. Math. Soc.43 (1937), 293–298.

    Article  MATH  MathSciNet  Google Scholar 

  93. R. M. Wilson,Nonisomorphic Steiner triple systems, Math. Z.135 (1974), 303–313.

    Article  MATH  Google Scholar 

  94. E. Bammel and J. Rothstein,The number of 9×9 Latin squares, Discrete Math. 11 (1975), 93–95.

    Article  MATH  MathSciNet  Google Scholar 

  95. S. Burris,Abstract 75T-A104, Notices American Math. Soc.22 (1975), A-439.

    MathSciNet  Google Scholar 

  96. R. Fagin,Monadic generalized spectra, etc., Z. Math. Logik Grundlagen Math.21 (1975), 89–96.

    MATH  MathSciNet  Google Scholar 

  97. L. T. Rigatelli,Sulle algebre α-diagonali, Rend. Mat., (6)7 (1974), 403–414.

    MathSciNet  Google Scholar 

  98. B. Jónsson, G. McNulty, and R. Quackenbush,The ascending and descending variental chains of a variety, Canad. J. Math.27 (1975), 25–31.

    MATH  MathSciNet  Google Scholar 

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    Walter Taylor

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Taylor, W. The fine spectrum of a variety. Algebra Universalis 5, 263–303 (1975). https://doi.org/10.1007/BF02485261

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