Commutative weakly nil-neat group rings

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. Math., Tokushima Univ., 2019), related to commutative nil-clean, weakly nil-clean and nil-neat group rings, respectively.

Keywords:

• Group rings
• (weakly) nil-clean rings
• (weakly) nil-neat rings

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20C07
• 16U60
• 16S34

Additional information

Funding

The work of the corresponding author (P. V. Danchev) is partially supported by the Bulgarian National Science Fund under Grant KP-06 N 32/1 of Dec. 07, 2019.