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Mat. Sb. (N.S.), 1987, Volume 133(175), Number 2(6), Pages 154–166 (Mi msb2541)  

This article is cited in 23 scientific papers (total in 23 papers)

Inherently nonfinitely based finite semigroups

M. V. Sapir


Abstract: A locally finite variety is called inherently nonfinitely based if it is not contained in any finitely based locally finite variety. A finite universal algebra is called inherently nonfinitely based if it generates an inherently nonfinitely based variety. In this paper a description of inherently nonfinitely based finite semigroups is given; it is proved that the set of such semigroups is recursive and that the property of a finite semigroup to be inherently nonfinitely based is mainly determined by the structure of its subgroups. It is also shown that there exists a unique minimal inherently nonfinitely based variety of semigroups consisting not only of groups. It is not known whether there exists an inherently nonfinitely based variety of groups.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 61:1, 155–166

Bibliographic databases:

UDC: 512.53
MSC: 20M07
Received: 31.01.1986

Citation: M. V. Sapir, “Inherently nonfinitely based finite semigroups”, Mat. Sb. (N.S.), 133(175):2(6) (1987), 154–166; Math. USSR-Sb., 61:1 (1988), 155–166

Citation in format AMSBIB
\Bibitem{Sap87}
\by M.~V.~Sapir
\paper Inherently nonfinitely based finite semigroups
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 133(175)
\issue 2(6)
\pages 154--166
\mathnet{http://mi.mathnet.ru/msb2541}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=905002}
\zmath{https://zbmath.org/?q=an:0655.20045|0634.20027}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 61
\issue 1
\pages 155--166
\crossref{https://doi.org/10.1070/SM1988v061n01ABEH003199}


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    Citing articles on Google Scholar: Russian citations, English citations
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    1. Baker K. Mcnulty G. Taylor W., “Growth Problems for Avoidable Words”, Theor. Comput. Sci., 69:3 (1989), 319–345  crossref  mathscinet  zmath  isi
    2. George F. McNulty, “A field guide to equational logic”, Journal of Symbolic Computation, 14:4 (1992), 371  crossref
    3. L. N. Shevrin, “On the theory of epigroups. I”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 485–512  mathnet  crossref  mathscinet  zmath  isi
    4. Margolis S., Sapir M., “Quasi-Identities of Finite-Semigroups and Symbolic Dynamics”, Isr. J. Math., 92:1-3 (1995), 317–331  crossref  mathscinet  zmath  isi
    5. OLGA SAPIR, “FINITELY BASED WORDS”, Int. J. Algebra Comput, 10:04 (2000), 457  crossref
    6. MARCEL JACKSON, OLGA SAPIR, “FINITELY BASED, FINITE SETS OF WORDS”, Int. J. Algebra Comput, 10:06 (2000), 683  crossref
    7. Jackson M., “Finite Semigroups Whose Varieties Have Uncountably Many Subvarieties”, J. Algebra, 228:2 (2000), 512–535  crossref  mathscinet  zmath  isi
    8. Jackson M., “Small Semigroup Related Structures with Infinite Properties”, Bull. Aust. Math. Soc., 61:3 (2000), 525–527  crossref  zmath  isi
    9. Crvenkovic S., Dolinka I., Vincic M., “Equational Bases for Some 0-Direct Unions of Semigroups”, Stud. Sci. Math. Hung., 36:3-4 (2000), 423–431  crossref  mathscinet  zmath  isi
    10. Jackson M., “Small Inherently Nonfinitely Based Finite Semigroups”, Semigr. Forum, 64:2 (2002), 297–324  crossref  mathscinet  zmath  isi
    11. M. V. Volkov, I. A. Gol'dberg, “Identities of Semigroups of Triangular Matrices over Finite Fields”, Math. Notes, 73:4 (2003), 474–481  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. MARCEL JACKSON, RALPH McKENZIE, “INTERPRETING GRAPH COLORABILITY IN FINITE SEMIGROUPS”, Int. J. Algebra Comput, 16:01 (2006), 119  crossref
    13. Bergman G.W., “Problem List From Algebras, Lattices and Varieties: a Conference in Honor of Walter Taylor, University of Colorado, 15-18 August, 2004”, Algebr. Universalis, 55:4 (2006), 509–526  crossref  mathscinet  zmath  isi
    14. Dolinka I., “A Nonfinitely Based Finite Semiring”, Int. J. Algebr. Comput., 17:8 (2007), 1537–1551  crossref  mathscinet  zmath  isi
    15. EDMOND W. H. LEE, “COMBINATORIAL REES–SUSHKEVICH VARIETIES ARE FINITELY BASED”, Int. J. Algebra Comput, 18:05 (2008), 957  crossref
    16. McNulty G.F., Szekely Z., Willard R., “Equational Complexity of the Finite Algebra Membership Problem”, Int. J. Algebr. Comput., 18:8 (2008), 1283–1319  crossref  mathscinet  zmath  isi
    17. Dolinka I., “A Class of Inherently Nonfinitely Based Semirings”, Algebr. Universalis, 60:1 (2009), 19–35  crossref  mathscinet  zmath  isi
    18. Marcel Jackson, Belinda Trotta, “The Division Relation: Congruence Conditions and Axiomatisability”, Comm. in Algebra, 38:2 (2010), 534  crossref
    19. A. V. Tishchenko, “A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups”, J. Math. Sci., 186:4 (2012), 667–681  mathnet  crossref
    20. Edmond W. H. Lee, “Varieties generated by 2-testable monoids”, Studia Scientiarum Mathematicarum Hungarica, 49:3 (2012), 366  crossref
    21. A. V. Tishchenko, “On the lattice of subvarieties of the wreath product the variety of semilattices and the variety of semigroups with zero multiplication”, J. Math. Sci., 221:3 (2017), 436–451  mathnet  crossref  mathscinet
    22. Olga Sapir, “Non-finitely based monoids”, Semigroup Forum, 2015  crossref
    23. I. M. Isaev, A. V. Kislitsin, “Tozhdestva vektornykh prostranstv, vlozhennykh v lineinye algebry”, Sib. elektron. matem. izv., 12 (2015), 328–343  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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