Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T00:55:20.086Z Has data issue: false hasContentIssue false

Completely right injective semigroups that are unions of groups

Published online by Cambridge University Press:  18 May 2009

E. H. Feller
Affiliation:
University of Wisconsin, Milwaukee, U.S.A.
R. L. Gantos
Affiliation:
University of Wisconsin, Milwaukee, U.S.A.
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.

A semigroup S with 0 and 1 is termed completely right injective provided every right unitary S-system is injective. A necessary condition for a semigroup to be com-pletely right injective is given in [2]; namely, every right ideal is generated by an idempotent. An example in section 3 of this paper shows the existence of semigroups with 0 and 1 satisfying this condition which are not completely right injective. In [3], it is shown that the condition that every right and left ideal is generated by an idempotent is necessary and sufficient in the case that S is both completely right and left injective (called completely injective). Such a semigroup is an inverse semigroup with 0 whose idempotents are dually well-ordered.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Amer. Math. Soc. Mathematical Surveys 7, Vol. I (Providence, R. I., 1961).Google Scholar
2.Feller, E. H. and Gantos, R. L., Completely injective semigroups with central idempotents, Glasgow Math. J. 10 (1969), 1620.Google Scholar
3.Feller, E. H. and Gantos, R. L., Completely injective semigroups, Pacific J. Math. 31 (1969), 359366.CrossRefGoogle Scholar