×

Limit varieties of aperiodic monoids with commuting idempotents. (English) Zbl 1509.20076

Summary: A variety of algebras is called limit if it is nonfinitely-based but all its proper subvarieties are finitely-based. A monoid is aperiodic if all its subgroups are trivial. We classify all limit varieties of aperiodic monoids with commuting idempotents.

MSC:

20M07 Varieties and pseudovarieties of semigroups

References:

[1] S. V. Gusev, A new example of a limit variety of monoids, Semigroup Forum, accepted, doi: 10.1007/s00233-019-10078-1. · Zbl 1508.20075
[2] Gusev, S. V. and Vernikov, B. M., Chain varieties of monoids, Dissertat. Math.534 (2018) 1-73. · Zbl 1434.20042
[3] Jackson, M., Finiteness properties of varieties and the restriction to finite algebras, Semigroup Forum70 (2005) 154-187. · Zbl 1073.20052
[4] Jackson, M. and Sapir, O., Finitely based, finite sets of words, Int. J. Algebra Comput.10 (2000) 683-708. · Zbl 0980.20052
[5] Kozhevnikov, P. A., On nonfinitely based varieties of groups of large prime exponent, Commun. Algebra40 (2012) 2628-2644. · Zbl 1259.20034
[6] Lee, E. W. H., Finitely generated limit varieties of aperiodic monoids with central idempotents, J. Algebra Appl.40 (2009) 779-796. · Zbl 1193.20066
[7] Lee, E. W. H., Maximal Specht varieties of monoids, Moscow Math. J.12 (2012) 787-802. · Zbl 1295.20063
[8] Lee, E. W. H., On certain Cross varieties of aperiodic monoids with commuting idempotents, Res. Math.66 (2014) 491-510. · Zbl 1321.20049
[9] Lee, E. W. H. and Li, J. R., Minimal non-finitely based monoids, Dissertat. Math.475 (2011) 1-65. · Zbl 1238.20067
[10] Perkins, P., Bases for equational theories of semigroups, J. Algebra11 (1969) 298-314. · Zbl 0186.03401
[11] Pollák, G., On two classes of hereditarily finitely based semigroup identities, Semigroup Forum25 (1982) 9-33. · Zbl 0496.20042
[12] Sapir, O. B., Lee monoids are nonfinitely based while the sets of their isoterms are finitely based, Bull. Aust. Math. Soc.97(3) (2018) 422-434. · Zbl 1442.20034
[13] O. B. Sapir, Limit varieties of \(J\)-trivial monoids, to appear; available at: https://arxiv.org/abs/2003.09950v2. · Zbl 1508.20079
[14] L. N. Shevrin and M. V. Volkov, Identities of semigroups, Izv. VUZ. Mat.11 (1985) 3-47 [Russian; Engl. translation: Soviet Math. Izv. VUZ29(11) (1985) 1-64]. · Zbl 0629.20029
[15] Volkov, M. V., The finite basis problem for finite semigroups, Sci. Math. Jpn.53 (2001) 171-199. · Zbl 0990.20039
[16] Wismath, S. L., The lattice of varieties and pseudovarieties of band monoids, Semigroup Forum33 (1986) 187-198. · Zbl 0591.20060
[17] W. T. Zhang and Y. F. Luo, A new example of limit variety of aperiodic monoids, to appear; available at: https://arxiv.org/abs/1901.02207.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.