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FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS (2007)
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BibTeX
@MISC{Gomes07fundamentalsemigroups,
author = {Gracinda M. S. Gomes and Victoria Gould},
title = {FUNDAMENTAL SEMIGROUPS HAVING A BAND OF IDEMPOTENTS},
year = {2007}
}
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Abstract
The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider are weakly B-abundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S) = B lies in our class. On the other hand, if a semigroup S lies in our class, then S is Ehresmann if and only if B is a semilattice. The Hall semigroup WB is a subsemigroup of SB, as are the (weakly) idempotent connected semigroups VB and UB. We show how the structure of SB can be used to extract information relating to arbitrary weakly B-abundant semigroups with (C).
