Hostname: page-component-6d856f89d9-26vmc Total loading time: 0 Render date: 2024-07-16T05:02:41.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Idempotent-separating extensions of regular semigroups with Abelian kernel

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

M. Loganathan
M. Loganathan
Affiliation:
Ramanujan Institute of Mathematics, University of Madras, Madras-600 005, India
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.

Let S be a regular semigroup and D(S) its associated category as defined in Loganathan (1981). We introduce in this paper the notion of an extension of a D(S)-module A by S and show that the set Ext(S, A) of equivalence classes of extensions of A by S forms an abelian group under a Baer sum. We also study the functorial properties of Ext(S, A).

MSC classification

Secondary: 20M50: Connections of semigroups with homological algebra and category theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 104 - 113
Copyright
Copyright © Australian Mathematical Society 1982

References

Lallement, G. (1967), ‘Demi-groupes réguliers’, Ann. Mat. Pura Appl. 87, 47–130.CrossRefGoogle Scholar
Lausch, H. (1975), ‘Cohomology of inverse semigroups’, J. Algebra 35, 273–303.CrossRefGoogle Scholar
Leech, J. (1975), ‘H-coextensions of monoids’, Mem. Amer. Math. Soc. 1, no. 157 (Amer. Math. Soc., Providence, R.I..).Google Scholar
Loganathan, M. (1981), ‘Cohomology of inverse semigroups’, to appear.CrossRefGoogle Scholar
Lane, S. Mac (1963), Homology (Springer-Verlag, New York).CrossRefGoogle Scholar
Lane, S. Mac (1971), Categories for the working mathematician (Springer-Verlag, New York).CrossRefGoogle Scholar
Nambooripad, K. S. S. (1979), ‘Structure of regular semigroups I’, Mem. Amer. Math. Soc. 22, no. 224 (Amer. Math. Soc., Providence, R.I.).Google Scholar
Sribala, S. (1977), ‘Cohomology and extension of inverse semigroup’, J. Algebra 47, 1–17.CrossRefGoogle Scholar