2019/12/05 by Peter Danchev, Danchev, Peter V.
Mathematics · #13B99 #16E50 #16U99 #16W10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1912.02579
openalex publication_date 2019/12/05 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We introduce and investigate the so-called D-regularly nil clean rings by showing that these rings are, in fact, a non-trivial generalization of the classical von Neumann regular rings and of the strongly π-regular rings. Some other close relationships with certain well-known classes of rings such as π-regular rings, exchange rings, clean rings, nil-clean rings, etc., are also demonstrated. These results somewhat supply a recent publication of the author in Turk. J. Math. (2019) as well as they somewhat expand the important role of the two examples of nil-clean rings obtained by Ster in Lin. Algebra & Appl. (2018). Likewise, the obtained symmetrization supports that for exchange rings established by Khurana et al. in Algebras & Represent. Theory (2015).