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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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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
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\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
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=897000}
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\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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This publication is cited in the following articles:
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M. V. Sapir, “Inherently nonfinitely based finite semigroups”, Math. USSR-Sb., 61:1 (1988), 155–166
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M. V. Sapir, “The restricted Burnside problem for varieties of semigroups”, Math. USSR-Izv., 38:3 (1992), 659–667
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Jennifer Hyndman, Ralph McKenzie, Walter Taylor, “
k-ary monoids of term operations”, Semigroup Forum, 44:1 (1992), 21
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George F. McNulty, “A field guide to equational logic”, Journal of Symbolic Computation, 14:4 (1992), 371
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Robert Cacioppo, “Nonfinitely based pseudovarieties and inherently nonfinitely based varieties”, Semigroup Forum, 47:1 (1993), 223
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L. N. Shevrin, “On the theory of epigroups. I”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 485–512
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Marcel Jackson, “Small semigroup related structures with infinite properties”, BAZ, 61:3 (2000), 525
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Marcel Jackson, “Finite Semigroups Whose Varieties Have Uncountably Many Subvarieties”, Journal of Algebra, 228:2 (2000), 512
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MARCEL JACKSON, OLGA SAPIR, “FINITELY BASED, FINITE SETS OF WORDS”, Int. J. Algebra Comput, 10:06 (2000), 683
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OLGA SAPIR, “FINITELY BASED WORDS”, Int. J. Algebra Comput, 10:04 (2000), 457
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V. Yu. Popov, “Markov Properties of Burnside Varieties of Semigroups”, Algebra and Logic, 42:1 (2003), 54–60
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M. V. Volkov, I. A. Gol'dberg, “Identities of Semigroups of Triangular Matrices over Finite Fields”, Math. Notes, 73:4 (2003), 474–481
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Charles C. Edmunds, Edmond W. H. Lee, Ken W. K. Lee, “Small Semigroups Generating Varieties with Continuum Many Subvarieties”, Order, 2010
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Edmond W. H. Lee, “Finite basis problem for 2-testable monoids”, centr eur j math, 2010
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Yanfeng Luo, Wenting Zhang, “On the variety generated by all semigroups of order three”, Journal of Algebra, 334:1 (2011), 1
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Edmond W. H. Lee, Jian Rong Li, Wen Ting Zhang, “Minimal non-finitely based semigroups”, Semigroup Forum, 2012
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Edmond W. H. Lee, “Varieties generated by 2-testable monoids”, Studia Scientiarum Mathematicarum Hungarica, 49:3 (2012), 366
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E.W.. H. Lee, W.T.ing Zhang, “Finite basis problem for semigroups of order six”, LMS J. Comput. Math, 18:01 (2015), 1
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Olga Sapir, “Non-finitely based monoids”, Semigroup Forum, 2015
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D. V. Solomatin, “Planarnye mnogoobraziya polugrupp”, Sib. elektron. matem. izv., 12 (2015), 232–247
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I. M. Isaev, A. V. Kislitsin, “Tozhdestva vektornykh prostranstv, vlozhennykh v lineinye algebry”, Sib. elektron. matem. izv., 12 (2015), 328–343
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Jackson M., Lee E.W.H., “Monoid Varieties With Extreme Properties”, Trans. Am. Math. Soc., 370:7 (2018), 4785–4812
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Volkov M.V. Silva P.V. Soares F., “Local Finiteness For Green'S Relations in Semigroup Varieties”, Commun. Algebr., 46:11 (2018), 4625–4653
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