On the regularity of crossed products

TL;DR

This paper investigates the conditions under which generalized crossed product rings, especially twisted group rings over algebraically closed fields, exhibit properties like regularity, weak regularity, or absence of nilpotent elements.

Contribution

It provides necessary and sufficient conditions for twisted group rings over algebraically closed fields to be n-weakly regular, $\xi^* N$-rings, or nilpotent-free.

Findings

Characterizes when twisted group rings are n-weakly regular.

Identifies conditions for twisted group rings to be $\xi^* N$-rings.

Determines when such rings have no nilpotent elements.

Abstract

We study some generalizations of the notion of regular crossed products K*G. For the case when K is an algebraically closed field, we give necessary and sufficient conditions for the twisted group ring K*G to be an n-weakly regular ring, a $\xi^* N$-ring or a ring without nilpotent elements.