Locally adequate semigroup algebras

• Main Authors: Ji Yingdan, Luo Yanfeng
• Format: Article
• Language: English
• Published: De Gruyter 2016-01-01
• Series: Open Mathematics
• Subjects: contracted semigroup algebras; rukolaĭne idempotents; multiplicative basis; direct product decomposition; representation type; 16g30; 16g60
• Online Access: http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0004/math-2016-0004.xml?format=INT

We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant 0-J*$0{\rm{ - }}{\cal J}*$-simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the ℛ*${\cal R}*$-classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.