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Idempotent-separating extensions of regular semigroups

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  • A. Tamilarasi

Abstract

For a regular biordered set E , the notion of E -diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered set E , an E -diagram in a category C is a collection of objects, indexed by the elements of E and morphisms of C satisfying certain compatibility conditions. With such an E -diagram A we associate a regular semigroup Reg E ( A ) having E as its biordered set of idempotents. This regular semigroup is analogous to automorphism group of a group. This paper provides an application of Reg E ( A ) to the idempotent-separating extensions of regular semigroups. We introduced the concept of crossed pair and used it to describe all extensions of a regular semigroup S by a group E -diagram A . In this paper, the necessary and sufficient condition for the existence of an extension of S by A is provided. Also we study cohomology and obstruction theories and find a relationship with extension theory for regular semigroups.

Suggested Citation

  • A. Tamilarasi, 2005. "Idempotent-separating extensions of regular semigroups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-31, January.
    • Handle: RePEc:hin:jijmms:919565
    DOI: 10.1155/IJMMS.2005.2945
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