The Kernel of an Idempotent Separating Congruence on a Regular Semigroup

  • Francis J. Pastijn


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. [4]). 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 [6] 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.


Inverse Semigroup Regular Semigroup Group Morphism Identity Transformation Split Extension 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Francis J. Pastijn
    • 1
  1. 1.Dept. of Mathematics, Statistics and Computer ScienceMarquette UniversityMilwaukeeUSA

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