Jordan Nilpotent Group Rings of index $4$

TL;DR

This paper characterizes when the group ring of any group over a non-commutative ring is Jordan nilpotent of index 4, providing precise algebraic conditions for this property.

Contribution

It establishes necessary and sufficient conditions for the group ring to be Jordan nilpotent of index 4, extending understanding of algebraic structures in non-commutative ring theory.

Findings

Derived conditions for Jordan nilpotency of index 4

Generalized previous results to arbitrary groups and rings

Enhanced the classification of algebraic properties of group rings

Abstract

Let $RG$ be the group ring of an arbitrary group $G$ over an associative non-commutative ring $R$ with identity. In this paper, we have obtained the necessary and sufficient conditions under which $RG$ is Jordan nilpotent of index $4$.