2023/12/11 by Danchev, Peter, Javan, Arash, Moussavi, Ahmad
#16S34 #16U60 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2312.06257
Some variations of π-regular and nil clean rings were recently introduced in \cite5,8,7, respectively. In this paper, we examine the structure and relationships between these classes of rings. Specifically, we prove that (m, n)-regularly nil clean rings are left-right symmetric and also show that the inclusions (D-regularly nil clean) ⊆ (regularly nil clean) ⊆ ((m,n)-regularly nil clean) hold, as well as we answer Questions 1, 2 and 3 posed in \cite8. Moreover, some other analogous questions concerning the symmetric properties of certain classes of rings are treated as well by proving that centrally Utumi rings are always strongly π-regular.