Locally adequate semigroup algebras

Abstract

Abstract 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.