Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-12-02T21:50:57.557Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct finiteness of certain monoid algebras

Published online by Cambridge University Press:  20 January 2009

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland
Rights & Permissions [Opens in a new window]

Abstract

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 is said to be completely regular if and only if each of its elements lies in a subgroup. It is shown that the algebra of a completely regular monoid (semigroup with identity) over a field of characteristic zero is directly finite.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 365 - 369
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. 42 (1941), 1037–1049.CrossRefGoogle Scholar
2. Clifford, A. H. and Preston, G. B. The algebraic theory of semigroups, vol. 1 (Math. Surveys 7, Amer. Math. Soc., Providence R.I., 1961).Google Scholar
3. Kaplansky, I., Fields and rings (Chicago Lectures in Math., Univ. of Chicago, 1969).Google Scholar
4. Montgomery, M. S., Left and right inverses in group algebras, Bull. Amer. Math. Soc. 75 (1969), 539–540.CrossRefGoogle Scholar
5. Passman, D. S. The algebraic theory of group rings (Wiley-Interscience, New York, 1977).Google Scholar