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Bounded Baer-levi semigroups

Published online by Cambridge University Press:  09 April 2009

Diana Lindsey  and
Bernard Madison
Diana Lindsey
Affiliation:
Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A.
Bernard Madison
Affiliation:
University of South Alabama, Mobile, Alabama, 36688, U.S.A.
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Abstract

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Let p and q be infinite cardinal numbers, p ≧ q, X a set of cardinality p, and BL(X, p, q) the Baer-Levi semigroup of type (p, q) on X. Subsemigroups of BL(X, p, q) are defined and called bounded Baer-Levi semigroups. These semigroups are right simple and are universal in the embedding sense for the class of idempotent-free, right cancellative semigroups S so that any two elements of S have a common right identity in S. Further properties of bounded Baer-Levi semigroups are given and the structure of their lattices of congruences is discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 2 , March 1977 , pp. 183 - 193
Copyright
Copyright © Australian Mathematical Society 1977

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