OF SELF-INJECTIVE RINGS Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL
SOCIETY Volume 48, Number 2, April 1975 PROJECTIVE MAXIMAL RIGHT IDEALS OF …

ON SELF-INJECTIVE PERFECT RINGS Page 1 Canad. Math. Bull. Vol. 39 (1), 1996 pp. 55-58
ON SELF-INJECTIVE PERFECT RINGS DOLORS HERBERA AND AHMAD SHAMSUDDIN …

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 …

If R is a right non-singular ring (with 1) and Q is its (RE Johnson) maximal right quotient ring,
then the R-epimorphism∑ ipi⊗ qi→∑ piqi from (Q⊗ RQ) R to QR is not in general a …

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 …

Let R be an associative ring with identity. Then the left socle of R is a direct summand of R
as a right R-module if and only if it is projective as a left R-module and contains no infinite …

The class of simple right self-injective rings is divided into three subclasses: artinian; directly
finite (ie, xy= 1 implies yx= 1) but not artinian; and directly infinite. A number of properties …

A concept of “a prime ideal” in a commutative ring is extended to a general ring such that it
properly includes the class of maximal one sided ideals. Such a right (or left) ideal is called …

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 …

A ring extension S of a ring R is right intrinsic over R, in the sense of Faith and Utumi, if A∩
R≠ 0 for each nonzero right ideal A of S. S is a right quotient ring of R, in the sense of RE …