Primitive Orthogonal Idempotents Of Completely 0-simply Semigroup Algebras

Representation theory of semigroup algebras is an important research direction in semigroup algebraic theory and algebraic representation theory.A basic problem in the representation theory of semigroup algebras is how to find a complete set of primitive orthogonal idempotents of a semigroup algebra.In this paper,we first give a sufficient condition for a complete 0-simple semigroup algebra to have identity.Then we find a complete set of primitive orthogonal idempotents of this completely 0-simple semigroup algebras.Finally,two examples are given to calculate the complete sets of primitive orthogonal idempotents of such completely0-simple semigroup algebras.