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Fundamental semigroups

Published online by Cambridge University Press:  14 November 2011

P. M. Edwards
P. M. Edwards
Affiliation:
Department of Econometrics, Monash University, Clayton, Victoria, Australia 3168
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Synopsis

An idempotent-separating congruence μ is studied further in this paper. It is shown to satisfy special properties with respect to regular elements and to group-bound elements. It is shown that for any semigroup S, μ is the identity congruence on S/μ. From this, it can be shown that S/μ is fundamental for any semigroup S. Some alternative characterizations of μ are given and applied to yield sufficient conditions for a subsemigroup T of S to satisfy μ (T) = μ (S) ∩ (T × T), whence T is fundamental if S is fundamental.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 313 - 317
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

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