In a recent paper (which is to appear in J. Algebra Appl.) we proved that every element of a
right self-injective ring R is a sum of two units if and only if R has no factor ring isomorphic to …

It was proved independently by both Wolfson [An ideal theoretic characterization of the ring
of all linear transformations, Amer. J. Math. 75 (1953) 358–386] and Zelinsky [Every linear …

The purpose of this note is to provide examples of simple, right and left self-injective rings
which are not artinian, thus contradicting a theorem of S. Elliger [“On simple injective rings” …

LET Q be a prime regular right self-injective ring. By [2, Theorem 8] the ideals of Q are well
ordered by inclusion. Thus it is reasonable to try to classify Q in terms of simple right self …

A ring R is called right bounded if every essential right ideal contains a nonzero two-sided
ideal which is an essential ideal as a right ideal. If R is both right and left bounded, then we …

A ring R with unity is called right (left) self injective if the right (left) R-module R is injective
[7]. The purpose of this note is to prove the following: Let R be a prime ring with a maximal …

Although the notion of the maximal quotient ring of a nonsingular ring has been around for
some time, not much is known about its structure in general beyond the important theorems …

This paper is concerned with calculating centers of regular self-injective rings, particularly
those obtained by completions with respect to rank functions, and those obtained as factor …

Note that, if X is a subset of a ring R, l (X)(resp. r (X)) is just the left (resp. right) annihilator of
X in R since(RR)*= RR. We call a ring R right PF if every faithful right R-module is a …

Apart from von Neumann regular rings, rings with infinite identities have not been studied in
any detail. We take a first step in that direction by obtaining structure theorems for a class of …