ONE-SIDED UNIT-REGULAR IDEALS OF REGULAR RINGS

On unit-regular ideals

In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. It is shown that every square matrix over unit-regular ideals admits a diagonal reduction. We also prove that a regular ideal of a unital ring is unit-regular if and only if pseudo-similarity via the ideal is similarity. Let I be an ideal of a unital ring R. We...

Normal Ideals in Regular Rings

On One-Sided Ideals of Rings of Linear Transformations

Intuitionistic Fuzzy Ideals in Intra-regular Rings

The aim of this paper is to characterise intra-regular ring R by using the concept of intuitionistic fuzzy left(right,bi,quasi) ideals of R.

Commuting $pi$-regular rings

R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.