Commutative Weakly Nil-Neat Group Rings

TL;DR

This paper establishes a necessary and sufficient condition for when a commutative group ring RG is weakly nil-neat, expanding previous results on related algebraic structures by analyzing R, G, and their sections.

Contribution

It provides a new characterization of weakly nil-neat commutative group rings, extending prior work on nil-clean and nil-neat properties in algebra.

Findings

Characterizes weakly nil-neat group rings in terms of R, G, and their sections

Generalizes previous results on nil-clean and nil-neat group rings

Provides necessary and sufficient conditions for weakly nil-neat property

Abstract

Let R be a ring and let G be a group. We prove a rather curious necessary and sufficient condition for the commutative group ring RG to be weakly nil-neat only in terms of R,G and their sections. This somewhat expands three recent results, namely those established by McGovern et al. in (J. Algebra Appl., 2015), by Danchev-McGovern in (J. Algebra, 2015) and by the present authors in (J. Taibah Univ. Sci., 2020), related to commutative nil-clean, weakly nil-clean and nil-neat group rings, respectively.