S-Classification of Regular Semigroups |
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Authors: | Mario Petrich |
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Affiliation: | (1) 21420 Bol, Brac, Croatia |
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Abstract: | On any regular semigroup S, the greatest idempotent pure congruence
τ the greatest idempotent separating congruence μ and the least
band congruence β are used to give the S-classification of regular semigroups as follows. These congruences generate a sublattice
Λ of the congruence lattice C(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K- and T-relations
on C(S) to Λ. Such triples are characterized abstractly and form the objects of a category S whose morphisms are surjective K- and T-preserving homomorphisms subject to a mild condition. The class of regular semigroups
is made into a category S whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor
from S to S. The effect of the S-classification on Reilly semigroups and cryptogroups is discussed briefly. |
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Keywords: | |
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