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Embedding finite semigroup amalgams

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Jan Okniński  and
Mohan S. Putcha
Jan Okniński
Affiliation:
North carolina State UniversityRaleigh, North Carolina 27695-8205, U. S. A.
Mohan S. Putcha
Affiliation:
North carolina State UniversityRaleigh, North Carolina 27695-8205, U. S. A.
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Abstract

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Let S, T1,… Tk be finite semigroups and Ψ: S → Ti, be embeddings. When C[S] is semisimple, we find necessary and sufficient conditions for the semigroup amalgam (T1,…, Tk; S) to be embeddable in a finite semigroup. As a consequence we show that if S is a finite semigroup with C[S] semisimple, then S is an amalgamation base for the class of finite semigroups if and only if the principal ideals of S are linearly ordered. Our proof uses both the theory of representations by transformations and the theory of matrix representations as developed by Clifford, Munn and Ponizovskii

MSC classification

Secondary: 20M10: General structure theory 20M30: Representation of semigroups; actions of semigroups on sets 20M25: Semigroup rings, multiplicative semigroups of rings

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 489 - 496
Copyright
Copyright © Australian Mathematical Society 1991

References

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