Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T08:13:30.513Z Has data issue: false hasContentIssue false
  • English
  • Français

Some covering and embedding theorems for inverse semigroups

Published online by Cambridge University Press:  09 April 2009

D. B. McAllister
D. B. McAllister
Affiliation:
Department of Mathematical Sciences, Northern Illinois UniversityDeKalb, Illinois 60115U.S.A.
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.

An inverse semigroup S is called E-unitary if the equations ea = e = e2 together imply a2 = a. In a previous paper the author showed that every inverse semigroup is an idempotent separating homomorphic image of an E-unitary inverse semigroup. The main question considered in this paper is the following. Given an inverse semigroup S give a method for constructing E-unitary inverse semigroups P and idempotent separating homomorphisms φ P → S in such a way that the structure of P as a P-semigroup is evident.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 188 - 211
Copyright
Copyright © Australian Mathematical Society 1976

References

Ault, J. E. (1972), ‘Translational hull of an inverse semigroup’, Semigroup Forum 4, 165–168.CrossRefGoogle Scholar
Chen, S. Y. and Hseih, S. C. (1974), ‘Factorizable inverse semigroups’, Semigroup Forum, 8, 283–297.CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B. (1961), Algebraic Theory of Semigroups, Vol. 1, Math Surveys 7, (American Math. Soc., Providence, R. I.)CrossRefGoogle Scholar
McAllister, D. B. (1974), ‘Groups, semilattices and inverse semigroups’, Trans. American Math. Soc. 192, 227–244.Google Scholar
McAllister, D. B. (1974a), ‘Groups, semilattices and inverse semigroups, II’, Trans. American Math. Soc. 196, 351–370.CrossRefGoogle Scholar
McAllister, D. B. (1975), ‘One-to-one partial right translations of a right cancellative semigroup’, to appear J. Algebra.Google Scholar
McFadden, R. and O'Carroll, L. (1971), ‘F-inverse semigroups’, Proc. London Math. Soc. (3) 22, 652–666.CrossRefGoogle Scholar
O'Carroll, L., (1974), ‘Reduced inverse and partially ordered semigroups’, J. London Math. Soc. (2) 293–301.CrossRefGoogle Scholar
O'Carroll, L. (1975), ‘Embedding theorems for proper inverse semigroups’, submitted to J. Algebra.Google Scholar
Petrich, M. (1973), Introduction to Semigroups, Charles E. Marrill Publishing Company.Google Scholar
Reilly, N. R. (1974), ‘Extensions of congruences and homomorphisms to translational hulls’, Pacific J. Math. 54, 209–228.CrossRefGoogle Scholar
Saito, T. (1965), ‘Proper ordered inverse semigroups’, Pacific J. Math. 15, 649–666.CrossRefGoogle Scholar
Schein, B. M. (1973), ‘Completions, translational hulls and ideal extensions of inverse semigroups’, Czechoslovak Math. J. 575–609.Google Scholar