The Kernel of an Idempotent Separating Congruence on a Regular Semigroup

Francis J. Pastijn
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Francis J. Pastijn: Marquette University, Dept. of Mathematics, Statistics and Computer Science

A chapter in Lattices, Semigroups, and Universal Algebra, 1990, pp 203-210 from Springer

Abstract: Abstract 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.

Keywords: Inverse Semigroup; Regular Semigroup; Group Morphism; Identity Transformation; Split Extension (search for similar items in EconPapers)
Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2608-1_22

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DOI: 10.1007/978-1-4899-2608-1_22

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