Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-08T06:28:30.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Coperfect monoids

Published online by Cambridge University Press:  18 May 2009

Victoria Gould
Victoria Gould
Affiliation:
University of York
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper S will denote a given monoid, that is, a semigroup with an identity. A set A is a right S-system if there is a map φ: A × S → A satisfying

for any element a of A and any elements s, t of S. For φ(a, s) we write as and we refer to right S-systems simply as S-systems. One has the obvious definitions of an S-subsystem and an S-homomorphism.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 73 - 88
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Berthiaume, P., The injective envelope of S-sets, Canad. Math. Bull. 10 (1967), 261–273.CrossRefGoogle Scholar
2.Damiano, R. F., Coflat rings and modules, Pacific J. Math. 81 (1969), 349–369.CrossRefGoogle Scholar
3.Eklof, P. and Sabbagh, G., Model-completions and modules, Annals Math. Logic 2 (1970–1971), 251–295.CrossRefGoogle Scholar
4.Fountain, J. B., Completely right injective semigroups, Proc. London Math. Soc. 28 (1974), 28–44.CrossRefGoogle Scholar
5.Fountain, J. B., Perfect semigroups, Proc. Edinburgh Math. Soc. (2) 20 (1976–1977), 87–93.CrossRefGoogle Scholar
6.Gould, V. A. R., The characterisation of monoids by properties of their S-systems, Semigroup Forum 32 (1985), 251–265.CrossRefGoogle Scholar
7.Gould, V. A. R., Divisible S-systems and R-modules, Proc. Edinburgh Math. Soc. to appear.Google Scholar
8.Isbell, J. R., Beatific semigroups, J. Algebra 23 (1972), 228–238.CrossRefGoogle Scholar
9.Isbell, J. R., Perfect monoids, Semigroup Forum 2 (1971), 95–118.CrossRefGoogle Scholar
10.Normak, P., Purity in the category of M-sets, Semigroup Forum 20 (1980), 157–170.CrossRefGoogle Scholar
11.Shoji, K., Completely right injective semigroups, Math. Japon. 24 (1979–1980), 609–615.Google Scholar