Affiliation:
1. Institute of Mathematics and Informatics , Bulgarian Academy of Sciences , Sofia , Bulgaria
Abstract
Abstract
An arbitrary unital ring R is called feebly nil-clean if any its element is of the form q + e − f, where q is a nilpotent and e, f are idempotents with ef = fe. For any commutative ring R and any abelian group G, we find a necessary and sufficient condition when the group ring R(G) is feebly nil-clean only in terms of R, G and their sections. Our result refines establishments due to McGovern et al. in J. Algebra Appl. (2015) on nil-clean rings and Danchev-McGovern in J. Algebra (2015) on weakly nil-clean rings, respectively.
Reference11 articles.
1. [1] P. V. Danchev, Feebly nil-clean unital rings, Proc. Jangjeon Math. Soc., 21 (1) (2018), 155–165.10.12988/pms.2018.877
2. [2] P. V. Danchev, Feebly invo-clean unital rings, Ann. Univ. Sci. Budapest (Sect. Math.), 60 (2017), 85–91.
3. [3] P. V. Danchev and O. Al-Mallah, UU group rings, Eurasian Bull. Math., 1 (3) (2018), 85–88.
4. [4] P. V. Danchev and W. Wm. McGovern, Commutative weakly nil clean unital rings, J. Algebra, 425 (5) (2015), 410–422.10.1016/j.jalgebra.2014.12.003
5. [5] L. Fuchs, Abelian Groups, Springer Monographs in Math., Springer Internat. Publishing (Switzerland), 2015, 747 pp.10.1007/978-3-319-19422-6