International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 2945-2975
For a regular biordered set , the notion of -diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered set , an -diagram in a category is a collection of objects, indexed by the elements of and morphisms of satisfying certain compatibility conditions. With such an -diagram we associate a regular semigroup having as its biordered set of idempotents. This regular semigroup is analogous to automorphism group of a group. This paper provides an application of 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 -diagram . In this paper, the necessary and sufficient condition for the existence of an extension of by is provided. Also we study cohomology and obstruction theories and find a relationship with extension theory for regular semigroups.