Hostname: page-component-669899f699-2mbcq Total loading time: 0 Render date: 2025-04-27T12:19:00.346Z Has data issue: false hasContentIssue false
  • English
  • Français

On the semilattice of idempotents of a free inverse monoid

Published online by Cambridge University Press:  20 January 2009

Pedro V. Silva
Pedro V. Silva
Affiliation:
Deparamento de Matemática, Universidade do Porto, 4000 Porto, Portugal Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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.

Some new concepts are introduced, in particular that of a unique factorization semilattice. Necessary and sufficient conditions are given for two principal ideals of the semilattice of idempotents of a free inverse monoid FIM(X) to be isomorphic and some properties of the Munn semigroup of E[FIM(X)] are obtained. Some results on the embedding of semilattices in E[FIM(X)] are also obtained.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 2 , June 1993 , pp. 349 - 360
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Auslander, M. and Buchsbaum, D., Groups, rings, modules (Harper & Row 1974).Google Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups (Math. Surveys 7, Providence, R.I., Amer. Math. Soc, 1961 (vol. 1) and 1967 (vol. II)).CrossRefGoogle Scholar
3.Howie, J. M., Introduction to semigroup theory (Academic Press 1976).Google Scholar
4.Munn, W. D., Fundamental inverse semigroups, Quart. J. Math. Oxford (2) 21 (1970), 157–170.CrossRefGoogle Scholar
5.Munn, W. D., Free inverse semigroups, Proc. London Math. Soc. (3) 29 (1974), 385–404.CrossRefGoogle Scholar
6.Petrich, M., Inverse semigroups (Wiley 1984).Google Scholar
7.Reilly, N. R., Free generators in free inverse semigroups, Bull. Austral. Math. Soc. 7 (1972), 407–424; correction: Bull. Austral. Math. Soc. 9 (1973), 479.CrossRefGoogle Scholar
8.Scheiblich, H. E., Free inverse semigroups, Proc. Amer. Math. Soc. 38 (1973), 1–7.CrossRefGoogle Scholar