Year: 2010
Author: Yonghua Li, Yong He
Communications in Mathematical Research , Vol. 26 (2010), Iss. 4 : pp. 289–303
Abstract
In this paper we establish a construction of a class of left $E$-adequate semigroups by using semilattices of cancellative monoids and fundamental left $E$-adequate semigroups. We first introduce concepts of type $µ^+$ ($µ^∗$, $µ$) abundant semigroups and type $µ^+$ left $E$-adequate semigroups. In fact, regular semigroups are type $µ^+$ abundant semigroups and inverse semigroups are type $µ^+$ left $E$-adequate semigroups. Next, we construct a special kind of algebras called $E^+$-product. It is proved that every $E^+$-product is a type $µ^+$ left $E$-adequate semigroup, and every type $µ^+$ left $E$-adequate semigroup is isomorphic to an $E^+$-product of a semilattice of cancellative monoids with a fundamental left $E$-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an $E^+$-product of a Clifford semigroup by a fundamental inverse semigroup.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19127
Communications in Mathematical Research , Vol. 26 (2010), Iss. 4 : pp. 289–303
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: type $µ^+$ semigroup abundant semigroup left $E$-adequate semigroup $E^+$-product.