Artinian Semigroup-Graded Rings

Abstract

Let S be a semigroup with no infinite subgroups and let R be a right Artinian S-graded ring. We prove that R necessarily has finite support.

Semigroup rings with certain finiteness conditions

“…In view of this, it is natural to consider skew semigroup rings and semigroup graded rings only for such semigroups that have no infinite subgroups. A powerful generalization of Zelmanov's theorem was obtained in [4]; the proof of this result does not use parts of the preceding proofs.…”