A Class of Left $E$-Adequate Semigroups

A Class of Left $E$-Adequate Semigroups

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.

Author Details

Yonghua Li

Yong He