Affiliation:
1. Universität-Gesamthochschule Kassel, Fachbereich 17 Mathematik/Informatik, Holländische Str. 36, D-34109 Kassel, Germany
Abstract
Let V be a variety of regular orthogroups, i.e. completely regular orthodox semigroups whose band of idempotents is regular. Let S be an orthodox semigroup which is a (normal) extension of an orthogroup K from V by an inverse semigroup G, that is, there is a congruence ρ on S such that the semigroup ker ρ of all idempotent related elements of S is isomorphic to K and S/ρ≅G. It is shown that S can be embedded into an orthodox subsemigroup T of a double semidirect product A**G where A belongs to V. Moreover T itself can be chosen to be an extension of a member from V by G. If in addition ρ is a group congruence we obtain a recent result due to M.B. Szendrei [16] which says that each orthodox semigroup which is an extension of a regular orthogroup K by a group G can be embedded into a semidirect product of an orthogroup K′ by G where K′ belongs to the variety of orthogroups generated by K.
Publisher
World Scientific Pub Co Pte Lt
Cited by
4 articles.
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