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Extensions of a Brandt Semigroup by Another

Published online by Cambridge University Press:  20 November 2018

Gérard Lallement  and
Mario Petrich
Gérard Lallement
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
Mario Petrich
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
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One possible first step in considering the structure of a class of semigroups is to study the ideal extensions (here simply called “extensions“) of simple or 0-simple semigroups in by another if the latter are of known structure. Extensions of a semigroup by another were first studied by Clifford (see [1, 4.4 and 4.5]). In his constructions, an extension of a semigroup S by a semigroup T with zero is given by a function (satisfying certain conditions) from T* = T\0 into the translational hull of S.

We use certain results (refining those of Clifford) established in [2] and a description of the translational hull of a Brandt semigroup given in [9] (see also [8]), to construct all extensions V of a Brandt semigroup S having a finite number of idempotents by any Brandt semigroup T (cf. [10]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 974 - 983
Copyright
Copyright © Canadian Mathematical Society 1970

References

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