FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 4, PAGES 1227-1233

On the nilpotency of subrings of skew group rings

V. A. Mushrub

Abstract

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The main aim of the present paper is to prove the following theorem.

Theorem. Let $A$ be either a left Goldie ring or a ring satisfying the ascending chain conditions both for left and for right annihilators, $G$ be a free commutative group and $\sigma :\; G\; \to \; Aut(A)$ be a group homomorphism. Then any homogeneous nilsubsemigroup of the multiplicative semigroup of the skew group ring $A$_s[G] is nilpotent.

This theorem can be considered as a skew analogue of a well-known classical result in the ring theory, Shock--Fisher theorem.

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Last modified: March 19, 2005