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A Syntactic approach to covers for E-dense semigroups over group varieties

journal contribution
posted on 2023-05-16, 12:44 authored by Auinger, K, Trotter, PG
A major result of D. B. McAlister is that every inverse semigroup is an idempotent separating morphic image of an E-unitary inverse semigroup. The result has been generalized by various authors (including Szendrei, Takizawa, Trotter, Fountain, Almeida, Pin, Weil) to any semigroup of the following types: orthodox, regular, E-dense with commuting idempotents, E-dense with idempotents forming a subsemigroup, and E-dense. In each case, a semigroup is a morphic image of a semigroup in which the weakly self conjugate core is unitary and separated by the homomorphism. In the present paper, for any variety H of groups and any E-dense semigroup S, the concept of an "H-verbal subsemigroup" of S is introduced which is intimately connected with the least H-congruence on S. What is more, this construction provides a short and easy access to covering results of the aforementioned kind. Moreover, the results are generalized, in that covers over arbitrary group varieties are constructed for any E-dense semigroup. If the given semigroup enjoys a "regularity condition" such as being eventually regular, group bound, or regular, then so does the cover.

History

Publication title

Mathematika

Volume

48

Issue

95-96

Pagination

231-245

ISSN

0025-5793

Department/School

School of Natural Sciences

Publisher

University College London

Place of publication

England

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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