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FINITE REGULAR BANDS ARE FINITELY RELATED

Part of: Semigroups Combinatorics

Published online by Cambridge University Press:  15 May 2012

IGOR DOLINKA
IGOR DOLINKA*
Affiliation:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia (email: [email protected])
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Abstract

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An algebra A is said to be finitely related if the clone Clo(A) of its term operations is determined by a finite set of finitary relations. We prove that each finite idempotent semigroup satisfying the identity xyxzx≈xyzx is finitely related.

Keywords

finite regular bandterm operationvarietyfinitely related

MSC classification

Secondary: 20M07: Varieties and pseudovarieties of semigroups 05A05: Permutations, words, matrices
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Aichinger, E., ‘Constantive Mal’cev clones on finite sets are finitely related’, Proc. Amer. Math. Soc. 138 (2010), 3501–3507.CrossRefGoogle Scholar
[2]Aichinger, E., Mayr, P. and McKenzie, R., ‘On the number of finite algebraic structures’, Preprint, arXiv:1103.2265.Google Scholar
[3]Biryukov, P. A., ‘Varieties of idempotent semigroups’, Algebra i Logika 9 (1970), 255–273, (in Russian).Google Scholar
[4]Brignall, R., Georgiou, N. and Waters, R. J., ‘Modular decomposition and the Reconstruction Conjecture’, Preprint, arXiv:1112.1509.Google Scholar
[5]Burris, S. and Sankappanavar, H. P., A Course in Universal Algebra, Graduate Texts in Mathematics, 78 (Springer, New York, 1981).CrossRefGoogle Scholar
[6]Davey, B. A., Jackson, M. G., Pitkethly, J. G. and Szabó, Cs., ‘Finite degree: algebras in general and semigroups in particular’, Semigroup Forum 83 (2011), 89–110.CrossRefGoogle Scholar
[7]Davey, B. A. and Knox, B. J., ‘From rectangular bands to k-primal algebras’, Semigroup Forum 64 (2002), 29–54.CrossRefGoogle Scholar
[8]Fennemore, C. F., ‘All varieties of bands I, II’, Math. Nachr. 48 (1971), 237–252, 253–262.CrossRefGoogle Scholar
[9]Gerhard, J. A., ‘The lattice of equational classes of idempotent semigroups’, J. Algebra 15 (1970), 195–224.CrossRefGoogle Scholar
[10]Gerhard, J. A. and Petrich, M., ‘Varieties of bands revisited’, Proc. Lond. Math. Soc. (3) 58 (1989), 323–350.CrossRefGoogle Scholar
[11]Kelly, P. J., ‘A congruence theorem for trees’, Pacific J. Math. 7 (1957), 961–968.CrossRefGoogle Scholar
[12]Marković, P., Maróti, M. and McKenzie, R., ‘Finitely related clones and algebras with cube terms’, Order, to appear.Google Scholar
[13]Mayr, P., ‘On finitely related semigroups’, manuscript (November, 2011), 20 pp.Google Scholar
[14]Petrich, M., ‘A construction and a classification of bands’, Math. Nachr. 48 (1971), 263–274.CrossRefGoogle Scholar
[15]Ulam, S. M., ‘A Collection of Mathematical Problems’, Interscience Tracts in Pure and Applied Mathematics, 8 (Interscience Publishers, New York–London, 1960).Google Scholar