关于分次 U-nil 洁净环

Nil-clean matrix rings

We characterize the nil clean matrix rings over fields. As a by product, it is proved that the full matrix rings with coefficients in commutative nil-clean rings are nil-clean, and we obtain a complete characterization of the finite rank Abelian groups with nil clean endomorphism ring and the Abelian groups with strongly nil clean endomorphism ring, respectively.

关于分次 NR-clean 环

On graded NR-clean rings

本文把 NR-clean 概念推广到分次环理论，定义分次 NR-clean 环，研究其性质、例子及在矩阵环、群环和平凡环扩张上的表现。

Commutative Weakly Nil-Neat Group Rings

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.