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A SUFFICIENT CONDITION UNDER WHICH A SEMIGROUP IS NONFINITELY BASED

Part of: Semigroups

Published online by Cambridge University Press:  11 November 2015

WEN TING ZHANG  and
YAN FENG LUO
WEN TING ZHANG*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou, Gansu 730000, PR China Department of Mathematics and Statistics, La Trobe University, VIC 3086, Australia email zhangwt@lzu.edu.cn
YAN FENG LUO
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou, Gansu 730000, PR China Department of Mathematics and Statistics, La Trobe University, VIC 3086, Australia email luoyf@lzu.edu.cn
*
✉zhangwt@lzu.edu.cn
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Abstract

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We give a sufficient condition under which a semigroup is nonfinitely based. As an application, we show that a certain variety is nonfinitely based, and we indicate the additional analysis (to be presented in a forthcoming paper), which shows that this example is a new limit variety of aperiodic monoids.

Keywords

semigroupidentityfinitely basedvariety

MSC classification

Primary: 20M07: Varieties and pseudovarieties of semigroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 454 - 466
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Almeida, J., Finite Semigroups and Universal Algebra (World Scientific, Singapore, 1994).Google Scholar
Burris, S. and Sankappanavar, H. P., A Course in Universal Algebra (Springer, New York, 1981).CrossRefGoogle Scholar
Edmunds, C. C., ‘Varieties generated by semigroups of order four’, Semigroup Forum 21 (1980), 67–81.CrossRefGoogle Scholar
Gupta, C. K. and Krasilnikov, A., ‘The finite basis question for varieties of groups—some recent results’, Illinois J. Math. 47 (2003), 273–283.Google Scholar
Jackson, M., ‘Finiteness properties of varieties and the restriction to finite algebras’, Semigroup Forum 70 (2005), 159–187.CrossRefGoogle Scholar
Kozhevnikov, P. A., ‘Varieties of groups of prime exponent and identities with high powers’, Candidate of Sciences Dissertation, Moscow State University, 2000 (in Russian).Google Scholar
Lee, E. W. H., ‘Finitely generated limit varieties of aperiodic monoids with central idempotents’, J. Algebra Appl. 8 (2009), 779–796.CrossRefGoogle Scholar
Lee, E. W. H., ‘Limit varieties generated by completely 0-simple semigroups’, Internat. J. Algebra Comput. 21 (2011), 257–294.CrossRefGoogle Scholar
Lee, E. W. H., ‘A sufficient condition for the nonfinite basis property of semigroups’, Monatsh. Math. 168 (2012), 461–472.Google Scholar
Lee, E. W. H. and Li, J. R., ‘Minimal nonfinitely based monoids’, Dissertationes Math. (Rozprawy Mat.) 475 (2011), 65.Google Scholar
Lee, E. W. H. and Volkov, M. V., ‘Limit varieties generated by completely 0-simple semigroups’, Internat. J. Algebra Comput. 21 (2011), 257–294.CrossRefGoogle Scholar
Lee, E. W. H. and Zhang, W. T., ‘Finite basis problem for semigroups of order six’, LMS J. Comput. Math. 18 (2015), 1–129.CrossRefGoogle Scholar
Newman, M. F., ‘Just non-finitely-based varieties of groups’, Bull. Aust. Math. Soc. 4 (1971), 343–348.CrossRefGoogle Scholar
Pollák, G., ‘A new example of limit variety’, Semigroup Forum 38 (1989), 283–303.CrossRefGoogle Scholar
Sapir, M. V., ‘On cross semigroup varieties and related questions’, Semigroup Forum 42 (1991), 345–364.CrossRefGoogle Scholar
Sapir, O., ‘Non-finitely based monoids’, Semigroup Forum 90 (2015), 557–586.Google Scholar
Volkov, M. V., ‘An example of a limit variety of semigroups’, Semigroup Forum 24 (1982), 319–326.CrossRefGoogle Scholar
Volkov, M. V., ‘The finite basis problem for finite semigroups’, Sci. Math. Jpn. 53 (2001), 171–199.Google Scholar
Zhang, W. T., ‘Existence of a new limit variety of aperiodic monoids’, Semigroup Forum 86 (2013), 212–220.Google Scholar
Zhang, W. T. and Luo, Y. F., A new example of limit variety of aperiodic monoids. Preprint.Google Scholar