2024/11/14 by Danchev, Peter, Javan, Arash, Hasanzadeh, Omid +2
#16S34 #16U60 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2411.09416
We study in-depth those rings R for which, there exists a fixed n≥ 1, such that un-1 lies in the subring Δ(R) of R for every unit u∈ R. We succeeded to describe for any n≥ 1 all reduced π-regular (2n-1)-ΔU rings by showing that they satisfy the equation x2n=x as well as to prove that the property of being exchange and clean are tantamount in the class of (2n-1)-ΔU rings. These achievements considerably extend results established by Danchev (Rend. Sem. Mat. Univ. Pol. Torino, 2019) and Koşan et al. (Hacettepe J. Math. & Stat., 2020). Some other closely related results of this branch are also established.