Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-06T01:10:59.262Z Has data issue: false hasContentIssue false
  • English
  • Français

Injective endomorphisms of 𝒢x-normal semigroups: finite defects

Published online by Cambridge University Press:  09 April 2009

Inessa Levi
Inessa Levi
Affiliation:
Department of Mathematics, University of Louisville, Louisville, KY, 40292
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 of transformations of an infinite set X is called 𝒢x-normal if S is invariant under conjugations by permutations of X. In this paper we describe injective endomorphisms of 𝒢x-normal semigroups of total one-to-one transformations f such that the range of f has a finite non-empty complement in X.

Keywords

semigroupGx-normal semigrouptransformationendomorphism.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 2 , October 1994 , pp. 261 - 280
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, volume 1 (Amer. Math. Soc., Providence, Rhode Island, 1961).Google Scholar
[2]Fröberg, R., Gottlieb, C. and Häggkvist, R., ‘On numerical semigroups’, Semigroup Forum 35 (1987), 63–83.Google Scholar
[3]Levi, I., ‘Automorphisms of normal transformation semigroups’, Proc. Edinburgh Math. Soc. Edinburgh Math. Notes 28 (1985), 185–205.Google Scholar
[4]Levi, I., ‘Normal semigroups of one-to-one transformations’, Proc. Edinburgh Math. Soc. Edinburgh Math. Notes 34 (1991), 65–76.Google Scholar
[5]Levi, I. and Schein, B. M., ‘The semigroup of all one-to-one transformations with finite defects’, Glasgow Math. J. (1989), 243–249.Google Scholar
[6]Magill, K. D. Jr, ‘Some homomorphism theorems for a class of semigroups’, Proc. London Math. Soc. (3) 15 (1965), 517–526.Google Scholar
[7]Sullivan, R. P., ‘Monomorphisms of transformation semigroups’, Semigroup Forum 32 (1985), 233–239.Google Scholar