Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-06T11:34:39.812Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroups of constant maps

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Boris M. Schein
Boris M. Schein
Affiliation:
Department of Mathematical SciencesUniversity of ArkansasFayetteville, Arkansas 72701, U.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.

In this paper “a map” denotes an arbitrary (everywhere defined, or partial, or even multi-valued) mapping. A map is constant if any two elements belonging to its domain have precisely the same images under this map. We characterize those semigroups which can be isomorphic to semigroups of constant maps or to involuted semigroups of constant maps.

Keywords

semigroupinvoluted semigroupsemigroup of binary relationsconstant mappings.

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 241 - 252
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Volume 1, (American Mathematical Society, Providence, R.I., 1961).CrossRefGoogle Scholar
[2]Lallement, G. and Petrich, M., ‘Décompositions I-matricielles d'un demi-groupe’, J. Math. Pures Appl. 45 (1966), 67–117.Google Scholar
[3]Munn, W. D., ‘Embedding semigroups in congruence-free semigroups’, Semigroup Forum 4 (1972), 46–60.CrossRefGoogle Scholar
[4]Schein, B. M., ‘Semigroups of rectangular binary relations’, Dokl. Akad. Nauk SSSR 165 (1965), 1011–1014 [Russian; for an English translation see:Google Scholar
Soviet Math. Dokl. 6 (1965), 1563–1566].Google Scholar
[5]Schein, B. M., ‘Relation algebras and function semigroups’, Semigroup Forum 1 (1970), 1–62.CrossRefGoogle Scholar
[6]Schein, B. M., ‘Bands with isomorphic endomorhpism semigroups’, J. Algebra (to appear).Google Scholar
[7]Tarski, A., ‘Contribution to the theory of models, II’, Nederl. Akad. Wetensch. Proc. Ser. A 57 (1954), 582–588.CrossRefGoogle Scholar