MMN-3724
n-fine rings
Nabil Zeidi;Abstract
A ring R is said to be n-fine if every nonzero element in R can be written as a sum of a nilpotent and n units in R. The class of these rings contains fine rings and n-good rings in which each element is a sum of n units. Fundamental properties of such rings are obtained. One of the main results of this paper is that the m x m matrix ring Mm(R) over any arbitrary ring R is 2-fine. Furthermore, the m x m matrix ring Mm(R) over a n-fine ring R is n-fine.
Vol. 24 (2023), No. 2, pp. 1073-1079
DOI: 10.18514/MMN.2023.3724