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Semigroup algebras of finite ample semigroups

Published online by Cambridge University Press:  21 March 2012

Xiaojiang Guo  and
Lin Chen
Xiaojiang Guo
Affiliation:
Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, People's Republic of China (xjguo@jxnu.edu.cn; chenlin621@163.com)
Lin Chen
Affiliation:
Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, People's Republic of China (xjguo@jxnu.edu.cn; chenlin621@163.com)
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Abstract

An adequate semigroup S is called ample if ea = a(ea)* and ae = (ae)†a for all a ∈ S and e ∈ E(S). Inverse semigroups are exactly those ample semigroups that are regular. After obtaining some characterizations of finite ample semigroups, it is proved that semigroup algebras of finite ample semigroups have generalized triangular matrix representations. As applications, the structure of the radicals of semigroup algebras of finite ample semigroups is obtained. In particular, it is determined when semigroup algebras of finite ample semigroup are semiprimitive.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 2 , April 2012 , pp. 371 - 389
Copyright
Copyright © Royal Society of Edinburgh 2012

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