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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

REFERENCES

[1]Fountain, J. B.. Completely right injective semigroups. Proc. London Math. Soc. (3) 28 (1974), 28–44.CrossRefGoogle Scholar
[2]Gould, V. A. R.. The characterization of monoids by properties of their S-systems. Semigroup Forum 32 (1985), 251–265.Google Scholar
[3]Gould, V. A. R.. Completely right pure monoids. Proc. Roy. Irish Acad. Sect. A 87 (1987), 73–82.Google Scholar
[4]Hall, T. E.. On regular semigroups. J. Algebra 24 (1973), 1–24.CrossRefGoogle Scholar
[5]Howie, J. M.. An Introduction to Semigroup Theory (Academic Press, 1976).Google Scholar
[6]Isbell, J. R.. Beatific semigroups. J. Algebra 23 (1972), 228–238.Google Scholar
[7]Munn, W. D.. Uniform semilattices and bisimple inverse semigroups. Quart. J. Math. Oxford Ser. (2) 17 (1966), 151–159.Google Scholar
[8]Normak, P.. Purity in the category of M-sets. Semigroup Forum 20 (1980), 157–170.Google Scholar
[9]Rosenstein, J. G.. Linear Orderings (Academic Press, 1982).Google Scholar
[10]Shoji, K.. Completely right injective semigroups. Math. Japon. 24 (1980), 609–615.Google Scholar