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Idempotent-generated regular semigroups

Published online by Cambridge University Press:  09 April 2009

C. Eberhart,
W. Williams and
L. Kinch
C. Eberhart
Affiliation:
University of KentuckyLexington, Kentucky 40506
W. Williams
Affiliation:
University of KentuckyLexington, Kentucky 40506
L. Kinch
Affiliation:
University of LouisvilleLouisville, Kentucky 40208 U.S.A.
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Suppose S is a regular semigroup and E is its set of idempotents. If E is subsemigroup of S, then S has been called orthodox and studied recently by Hall [3], Meakin [6], and Yamada [8]. In this paper we assume that E is not (necessarily) a subsemigroup of S and consider the subsemigroup generated by E, denoted <E>. If E denotes the set of all elements of S which can be written E, denoted <E>. If E denotes the set of all elements of S which can be written as the product of n (not necessarily distinct) idempotents of S, then . We show that <E> is always a regular subsemigroup of S and investigate relationships between it and S. The case where <E> = S is of particular interest to us; such semigroups will be referred to as idempotent-generated regular semi- groups.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973, pp. 27 - 34
Copyright
Copyright © Australian Mathematical Society 1973

References

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