Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-23T11:12:03.448Z Has data issue: false hasContentIssue false
  • English
  • Français

E-unitary inverse semigroups over semilattices

Published online by Cambridge University Press:  18 May 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115, 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.

An inverse semigroup is called E-unitary if the equations ea = e = e2 together imply a2 = a. In a previous paper [4], the author showed that any E-unitary inverse semigroup is isomorphic to a semigroup constructed from a triple (G, ℋ, ) consisting of a down-directed partially ordered set ℋ, an ideal and subsemilattice of ℋ and a group G acting on ℋ, on the left, by order automorphisms in such a way that ℋ = G. This semigroup is denoted by P(G, ℋ, ); it consists of all pairs (a, g)∈ × G such that g−1a ∈ , under the multiplication

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 1 , January 1978 , pp. 1 - 12
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vols. I and II, Math. Surveys of the Amer. Math. Soc. 7 (Providence, R.I., 1961 and 1967).Google Scholar
2.Eberhart, C. and Selden, J., One parameter inverse semigroups, Trans. Amer. Math. Soc. 168 (1972), 53–66.CrossRefGoogle Scholar
3.McAlister, D. B., Groups, semilattices and inverse semigroups, Trans. Amer. Math. Soc. 192 (1974), 227–244.Google Scholar
4.McAlister, D. B., Groups, semilattices and inverse semigroups II, Trans. Amer. Math. Soc. 196 (1974), 351–369.CrossRefGoogle Scholar
5.McAlister, D. B., Some covering and embedding theorems for inverse semigroups, J. Austral. Math. Soc. 22 (1976), 188–211.Google Scholar
6.McFadden, R. and O'Carroll, L., F-inverse semigroups, Proc. London Math. Soc. (3) 22 (1971), 652–666.CrossRefGoogle Scholar
7.Munn, W. D., A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc. 5 (1961), 41–48.CrossRefGoogle Scholar
8.O'Carroll, L., A note on free inverse semigroups, Proc. Edinburgh Math. Soc. (2) 19 (1974), 17–23.CrossRefGoogle Scholar
9.O'Carroll, L., Idempotent determined congruences on inverse semigroups, Semigroup Forum 12 (1976), 233–244.CrossRefGoogle Scholar
10.Reilly, N. R. and Munn, W. D., E-unitary congruences on inverse semigroups, Glasgow Math. J. 17 (1976), 57–75.Google Scholar
11.Reilly, N. R. and Scheiblich, H. E., Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar