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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 2, Pages 319–340 (Mi izv1296)  

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

Problems of Burnside type and the finite basis property in varieties of semigroups

M. V. Sapir


Abstract: Algorithms are found that determine, for a finite set of identities (balanced identities), whether every nil-semigroup (periodic semigorup) satisfying them is locally finite. A number of results on finitely based semigroup varieties are obtained as corollaries.
Bibliography: 34 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:2, 295–314

Bibliographic databases:

UDC: 512.513
MSC: Primary 20M07; Secondary 20M99
Received: 29.11.1984

Citation: M. V. Sapir, “Problems of Burnside type and the finite basis property in varieties of semigroups”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 319–340; Math. USSR-Izv., 30:2 (1988), 295–314

Citation in format AMSBIB
\Bibitem{Sap87}
\by M.~V.~Sapir
\paper Problems of Burnside type and the finite basis property in varieties of semigroups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 2
\pages 319--340
\mathnet{http://mi.mathnet.ru/izv1296}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=897000}
\zmath{https://zbmath.org/?q=an:0646.20047}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 2
\pages 295--314
\crossref{https://doi.org/10.1070/IM1988v030n02ABEH001012}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Sapir, “Inherently nonfinitely based finite semigroups”, Math. USSR-Sb., 61:1 (1988), 155–166  mathnet  crossref  mathscinet  zmath
    2. M. V. Sapir, “The restricted Burnside problem for varieties of semigroups”, Math. USSR-Izv., 38:3 (1992), 659–667  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Jennifer Hyndman, Ralph McKenzie, Walter Taylor, “ k-ary monoids of term operations”, Semigroup Forum, 44:1 (1992), 21  crossref  mathscinet  zmath  isi
    4. George F. McNulty, “A field guide to equational logic”, Journal of Symbolic Computation, 14:4 (1992), 371  crossref
    5. Robert Cacioppo, “Nonfinitely based pseudovarieties and inherently nonfinitely based varieties”, Semigroup Forum, 47:1 (1993), 223  crossref  mathscinet  zmath  isi
    6. L. N. Shevrin, “On the theory of epigroups. I”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 485–512  mathnet  crossref  mathscinet  zmath  isi
    7. Marcel Jackson, “Small semigroup related structures with infinite properties”, BAZ, 61:3 (2000), 525  crossref
    8. Marcel Jackson, “Finite Semigroups Whose Varieties Have Uncountably Many Subvarieties”, Journal of Algebra, 228:2 (2000), 512  crossref
    9. MARCEL JACKSON, OLGA SAPIR, “FINITELY BASED, FINITE SETS OF WORDS”, Int. J. Algebra Comput, 10:06 (2000), 683  crossref
    10. OLGA SAPIR, “FINITELY BASED WORDS”, Int. J. Algebra Comput, 10:04 (2000), 457  crossref
    11. V. Yu. Popov, “Markov Properties of Burnside Varieties of Semigroups”, Algebra and Logic, 42:1 (2003), 54–60  mathnet  crossref  mathscinet  zmath  elib
    12. 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
    13. Charles C. Edmunds, Edmond W. H. Lee, Ken W. K. Lee, “Small Semigroups Generating Varieties with Continuum Many Subvarieties”, Order, 2010  crossref  isi
    14. Edmond W. H. Lee, “Finite basis problem for 2-testable monoids”, centr eur j math, 2010  crossref
    15. Yanfeng Luo, Wenting Zhang, “On the variety generated by all semigroups of order three”, Journal of Algebra, 334:1 (2011), 1  crossref
    16. Edmond W. H. Lee, Jian Rong Li, Wen Ting Zhang, “Minimal non-finitely based semigroups”, Semigroup Forum, 2012  crossref
    17. Edmond W. H. Lee, “Varieties generated by 2-testable monoids”, Studia Scientiarum Mathematicarum Hungarica, 49:3 (2012), 366  crossref
    18. E.W.. H. Lee, W.T.ing Zhang, “Finite basis problem for semigroups of order six”, LMS J. Comput. Math, 18:01 (2015), 1  crossref
    19. Olga Sapir, “Non-finitely based monoids”, Semigroup Forum, 2015  crossref
    20. D. V. Solomatin, “Planarnye mnogoobraziya polugrupp”, Sib. elektron. matem. izv., 12 (2015), 232–247  mathnet  crossref
    21. I. M. Isaev, A. V. Kislitsin, “Tozhdestva vektornykh prostranstv, vlozhennykh v lineinye algebry”, Sib. elektron. matem. izv., 12 (2015), 328–343  mathnet  crossref
    22. Jackson M., Lee E.W.H., “Monoid Varieties With Extreme Properties”, Trans. Am. Math. Soc., 370:7 (2018), 4785–4812  crossref  isi
    23. Volkov M.V. Silva P.V. Soares F., “Local Finiteness For Green'S Relations in Semigroup Varieties”, Commun. Algebr., 46:11 (2018), 4625–4653  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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