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A Multiplication of E-Varieties of Regular Solid Semigroups by Inverse Semigroup Varieties (1997)
BibTeX
@MISC{Kuril97amultiplication,
author = {Martin Kuril},
title = {A Multiplication of E-Varieties of Regular Solid Semigroups by Inverse Semigroup Varieties},
year = {1997}
}
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Abstract
. A multiplication of e-varieties of regular E-solid semigroups by inverse semigroup varieties is described both semantically and syntactically. The associativity of the multiplication is also proved. 1. Introduction We investigate here an operator on the lattice of all e-varieties of regular semigroups. In [7] we defined semantically a partial multiplication on this lattice: U V is defined if U is an e-variety of regular semigroups and V is an e-variety of inverse semigroups. The definition is based on a certain semidirect product of regular semigroups by inverse semigroups. In the case that U is an e-variety of orthodox semigroups we also described our multiplication syntactically in terms of biinvariant congruences for orthodox semigroups introduced in [5] by Ka#ourek and Szendrei. In this paper we present a syntactical description of our multiplication in the case that the first factor is an e-variety of regular E-solid semigroups. The description is essentially based on the not...
