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@article{217411,
author = {Kaďourek, Jiří and Szendrei, Mária B.},
article_location = {New York},
article_number = {3},
keywords = {existence varieties of regular semigroups; bifree objects; regular E-solid semigroups; regular locally orthodox semigroups},
language = {eng},
issn = {0037-1912},
journal = {Semigroup Forum},
title = {On existence varieties of E-solid semigroups},
volume = {59},
year = {1999}
}
TY - JOUR
ID - 217411
AU - Kaďourek, Jiří - Szendrei, Mária B.
PY - 1999
TI - On existence varieties of E-solid semigroups
JF - Semigroup Forum
VL - 59
IS - 3
SP - 470
EP - 470
PB - Springer-Verlag
SN - 00371912
KW - existence varieties of regular semigroups
KW - bifree objects
KW - regular E-solid semigroups
KW - regular locally orthodox semigroups
N2 - Within the class of regular E-solid semigroups, a theory of e-varieties including appropriate notions of biidentities and biinvariant congruences is presented, such that, together with bifree objects, these notions inherit the properties and interrelations well known from universal algebra. This theory generalizes the previously developed such theory for orthodox semigroups.
As an application, the bifree objects in certain e-varieties of E-solid locally orthodox semigroups, which are constructed by means of Malcev products from varieties of bands, groups and completely simple semigroups, are described as subsemigroups in suitable Pastijn products of some bands by relatively bifree completely simple semigroups. As a consequence, it follows that every regular E-solid locally orthodox semigroup regularly divides a so-called solid Pastijn product of a band by a completely simple semigroup.
ER -
KAĎOUREK, Jiří a Mária B. SZENDREI. On existence varieties of E-solid semigroups. \textit{Semigroup Forum}. New York: Springer-Verlag, 1999, roč.~59, č.~3, s.~470-521. ISSN~0037-1912.
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