The Kernel of an Idempotent Separating Congruence on a Regular Semigroup
Let S be a regular semigroup and E(S) its set of idempotents. Let θ be an idempotent separating congruence on S. Traditionally by the kernel ker θ of θ we understand the union of the idempotent θ-classes (see e.g. ). For an idempotent separating congruence θ the idempotent θ-classes are groups, namely the θ-classes containing idempotents. The kernel normal system of θ considered by Preston in  is the set of these idempotent θ-classes and contains more information than the above mentioned ker θ, which, after all, is just a subset of S. In the following we shall adopt still another approach to the concept of the kernel of an idempotent separating congruence on a regular semigroup. We shall give a survey of some of the results obtained in collaboration with K. S. S. Nambooripad.
KeywordsInverse Semigroup Regular Semigroup Group Morphism Identity Transformation Split Extension
Unable to display preview. Download preview PDF.