When a group algebra (semigroup algebra) is an Artinian algebra? 
When a group algebra (semigroup algebra) is an Artinian algebra? 

We know that an Artinian algebra is an algebra that satisfies the descending chain condition on ideals. I think that a group algebra (semigroup algebra) is an Artinian algebra if the group algebra (semigroup algebra) satisfies the descending chain condition on ideals. Are there other equivalent conditions that determine when a group algebra (semigroup algebra) is an Artinian algebra? Thank you very much.

A result of E. Zelmanov (Zel'manov), Semigroup algebras with identities,
(Russian) Sib. Mat. Zh. 18, 787-798 (1977):
Assume that $kS$ is right artinian. Then $S$ is a finite semigroup. The converse holds if $S$ is monoid.
See this assertion in Jan Okniński, 
Semigroup algebras.Pure and Applied Mathematics, 138 (1990), p.172, Th.23.
