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Completely right pure monoids on which ℋ is a right congruence

Published online by Cambridge University Press:  24 October 2008

Victoria Gould
Victoria Gould
Affiliation:
Department of Mathematics, University of York
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Extract

An S-system over a monoid S is a set A together with a function ø: A × S → A such that (a, 1) ø = a and (a, st) ø = ((a, s) ø, t) ø for all a ∈ A and for all s, t ∈ S. So an S-system is a set on which S acts unitarily on the right. For (a, s) ø we write simply as: the notions of S-homomorphism, S-subsystem etc. are defined in the obvious manner. Many papers have been written characterizing monoids by properties of their S-systems; here we are concerned with injectivity and a related concept, absolute purity. Further details of the terms we use are given in Section 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 275 - 285
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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