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A Syntactic approach to covers for E-dense semigroups over group varieties
Citation
Auinger, K and Trotter, PG, A Syntactic approach to covers for E-dense semigroups over group varieties, Mathematika, 48, (95-96) pp. 231-245. ISSN 0025-5793 (2001) [Refereed Article]
DOI: doi:10.1112/S0025579300014467
Abstract
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.
Item Details
Item Type: | Refereed Article |
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Research Division: | Mathematical Sciences |
Research Group: | Pure mathematics |
Research Field: | Group theory and generalisations |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | Trotter, PG (Dr Peter Trotter) |
ID Code: | 21226 |
Year Published: | 2001 |
Web of Science® Times Cited: | 2 |
Deposited By: | Mathematics |
Deposited On: | 2003-08-01 |
Last Modified: | 2011-11-21 |
Downloads: | 0 |
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