A ring R is almost unit-clean provided that every element in R is equivalent to the sum of an idempotent and a regular element. We prove that every ring in which every zero-divisor is strongly pi-regular is almost unit-clean ...

An exchange ideal I of a ring R is locally comparable if for every regular x is an element of I there exists a right or left invertible u is an element of 1 + I such that x = xux. We prove that every matrix extension of ...

A ring R is defined to be J-normal if for any a, r∈ R and idempotent e∈ R, ae= 0 implies Rera⊆ J(R) , where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly normal rings and ...