Abstract
A nonempty subset X contained in anH-class of a regular semigroup S is called agroup coset in S if XX′X=X and X′XX′=X′ where X′ is the set of inverses of elements of X contained in anH-class of S. Let μ denote the maximum idempotent separating congruence on S. We show in Section 1 of this paper that the set K(S) of group cosets in S contained in the μ-classes of S is a regular semigroup with a suitably defined product. In Section 2, we describe subdirect products of twoinductive groupoids in terms of certain maps called ‘subhomomorphisms’. A special class of subdirect products, called S*-direct products, is described in Section 3. In the remaining two sections, we give some applications of the construction of S*-direct products for describing coextensions of regular semigroups and for providing a covering theorem for pseudo-inverse semigroups.
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Communicated by N.R. Reilly
Dedicated to Professor L.M. Gluskin on his 60th birthday
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Nambooripad, K.S.S., Veeramony, R. Subdirect products of regular semigroups. Semigroup Forum 27, 265–307 (1983). https://doi.org/10.1007/BF02572743
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DOI: https://doi.org/10.1007/BF02572743