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RP-dominated regular semigroups

Published online by Cambridge University Press:  14 November 2011

T. S. Blyth  and
J. B. Hickey
T. S. Blyth
Affiliation:
Mathematical Institute, University of St Andrews
J. B. Hickey
Affiliation:
Department of Mathematics, University of Glasgow
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Extract

We describe the structure of regular semigroups in which each element is dominated, in the Nambooripad order, by a unique maximal element that is ℋ-equivalent to a mididentity. These are precisely direct products of a rectangular band and a uniquely unit regular semigroup.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 185 - 191
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Ault, Janet E.. Semigroups with midunits. Trans. Amer. Math. Soc. 190 (1974)., 375–384.CrossRefGoogle Scholar
2Blyth, T. S. and McFadden, R.. Unit orthodox semigroups. Glasgow Math. J. 24 (1983)., 39–42.CrossRefGoogle Scholar
3Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups (Providence, R. I.: Amer. Math. Soc., 1961).Google Scholar
4Hickey, J. B.. Semigroups under a sandwich operation. Proc. Edinburgh Math. Soc. 26 (1983)., 371–382.CrossRefGoogle Scholar
5Howie, J. M.. An introduction to a semigroup theory (London: Academic Press, 1976).Google Scholar
6McFadden, R.. Unit regular orthodox semigroups. Glasgow Math. J. 25 (1984)., 229–240.CrossRefGoogle Scholar
7S, K.. Nambooripad, S.. The natural partial order on a regular semigroup. Proc. Edinburgh Math. Soc. 23 (1980)., 244–260.Google Scholar
8Yamada, Miyuki. A note on middle unitary semigroups. Kodai Math. Sem. Rep. 7 (1955)., 49–52.CrossRefGoogle Scholar