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Inverse subsemigroups of Rees matrix semigroups

Published online by Cambridge University Press:  17 April 2009

David E. Zitarelli
David E. Zitarelli
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA.
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Abstract

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According to the Sees Theorem, every completely 0-simple semigroup can be represented by a Rees matrix semigroup over a group with zero. A characterization of all subsemigroups of the latter is given in terms of the structure group, structure sets, and two mappings. Next all congruences on such subsemigroups are described, along with conditions for comparability. Finally, an algorithm for computing the number of nonisomorphic inverse subsemigroups is constructed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 445 - 463
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups Volume I (Math. Surveys 7 (I). Amer. Math. Soc., Providence, Rhode Island, 1961).Google Scholar
[2]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume II (Math. Surveys 7 (II). Amer. Math. Soc., Providence, Rhode Island, 1967).Google Scholar
[3]Hall, I.E., “On regular semigroups whose idempotents form a subsemigroup”, Bull. Austral. Math. Soc. 1 (1969), 195–208.CrossRefGoogle Scholar
[4]Petrich, Gérard Lallement et Mario, “Décompositions I-matricielles d'un demi-groupe”, J. Math. Purea Appl. 45 (1966), 67–117.Google Scholar
[5]Ляпин, Е.С. [Ljapin, E.S.], “Нормальные комплекоы асоциативных систем” [Normal complexes of associative systems], Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), 179–192.Google ScholarPubMed
[6]Lyapln, E.S., Aizenshtat, A.Ya., and Lesokhin, M.M., Exercises in group theory (translated by Zitarelli, David E.. Plenum Press, New York; Wolters-Noordhoff, Groningen, 1972).Google Scholar
[7]Petrich, Mario, Introduction to semigroups (Charles E. Merrill, Columbus, Ohio, 1973).Google Scholar
[8]Preston, G.B., “Congruences on Brandt semigroups”, Math. Ann. 139 (1959), 91–94.CrossRefGoogle Scholar
[9]Rees, D., “On semi-groups”, Proc. Cambridge Philos. Soc. 36 (1940), 387–400.CrossRefGoogle Scholar
[10]Tamura, T. and Chrislock, J.L., “Subsemigroups of completely 0-simple semigroups. I”, Proc. Japan Acad. 41 (1965), 128–131.Google Scholar
[11]Venkatesan, P.S., “On a class of inverse semigroups”, Amer. J. Math. 84 (1962), 578–582.CrossRefGoogle Scholar