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Rees matrix semigroups over inverse semigroups

Published online by Cambridge University Press:  14 November 2011

F. J. Pastijn  and
Mario Petrich
F. J. Pastijn
Affiliation:
Dienst Hogere Meetkunde, Rijksuniversiteit te Gent, Krijgslaan 281, B-9000 Gent, Belgium
Mario Petrich
Affiliation:
Dienst Hogere Meetkunde, Rijksuniversiteit te Gent, Krijgslaan 281, B-9000 Gent, Belgium
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Synopsis

A Rees matrix semigroup over an inverse semigroup contains a greatest regular subsemigroup. The regular semigroups obtained in this manner are abstractly characterized here. The greatest completely simple homomorphic image and the idempotent generated part of such semigroups are investigated. Rectangular bands of semilattices of groups and some special cases are characterized in several ways.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 61 - 90
Copyright
Copyright © Royal Society of Edinburgh 1986

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References

1Byleen, K.. Regular four-spiral semigroups, idempotent-generated semigroups and the Rees construction. Semigroup Forum 22 (1981), 97–100.CrossRefGoogle Scholar
2Fitz-Gerald, D. G.. On inverses of products of idempotents in regular semigroups. J. Austral. Math. Soc. 13 (1972), 335–337.CrossRefGoogle Scholar
3Hall, T. E.. Primitive homomorphic images of semigroups. J. Austral. Math. Soc. 8 (1968), 350–354.CrossRefGoogle Scholar
4Kim, J. B.. Idempotent-generated Rees matrix semigroups. Kyungpook Math. J. 10 (1970), 7–13.Google Scholar
5Lallement, G. and Petrich, M.. A generalization of the Rees theorem in semigroups. Acta Sci. Math (Szeged) 30 (1969), 113–132.Google Scholar
6Malcev, A. I.. The Metamathematics of Algebraic Systems (Studies in Logic and the Foundations of Mathematics) (Amsterdam: North Holland, 1971).Google Scholar
7McAlister, D. B.. Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups. J. Austral. Math. Soc. Ser. A 31 (1981), 325–336.CrossRefGoogle Scholar
8McAlister, D. B.. Rees matrix covers for locally inverse semigroups. Trans. Amer. Math. Soc. 277 (1983), 727–737.CrossRefGoogle Scholar
9Meakin, J.. The Rees construction in regular semigroups, preprint.Google Scholar
10Pastijn, F.. Rectangular bands of inverse semigroups. Simon Stevin 56 (1982), 3–95.Google Scholar
11Pastijn, F.. The structure of pseudo-inverse semigroups. Trans. Amer. Math. Soc. 273 (1982), 631–655.CrossRefGoogle Scholar
12Pastijn, F.. Regular locally testable semigroups as semigroups of quasi-ideals. Acta Math. Acad. Sci. Hungar. 36 (1980), 161–166.CrossRefGoogle Scholar
13Pastijn, F. and Petrich, M.. Straight locally inverse semigroups. Proc. London Math. Soc. (3) 49 (1984), 307–328.CrossRefGoogle Scholar
14Petrich, M.. Structure of Regular Semigroups (Montpellier: Cahiers Mathematiques, 1977).Google Scholar
15Petrich, M.. Lectures in Semigroups (London: Wiley, 1977).CrossRefGoogle Scholar
16Petrich, M.. Inverse Semigroups (New York: Wiley, 1984).Google Scholar
17Schein, B. M.. Completions, translational hulls and ideal extensions of inverse semigroups. Czechoslovak Math. J. 23 (1973), 575–610.CrossRefGoogle Scholar
18Yamada, M.. Regular semigroups whose idempotents satisfy permutation identities. Pacific J. Math. 21 (1967), 371–392.CrossRefGoogle Scholar