We show that if R is a ring such that each minimal left ideal is essential in a (direct)
summand of RR, then the dual of each simple right R-module is simple if and only if R is …

We show that ifRis a semiperfect ring with essential left socle andrl (K)= Kfor every small
right idealKofR, thenRis right continuous. Accordingly some well-known classes of rings …

CS rings and nakayama permutations Page 1 COMMUNICATIONS IN ALGEBRA, 25(12),
3787-3795 (1997) CS RINGS AND NAKAYAMA PERMUTATIONS Mohamed F. Yousif …

NONSINGULAR SEMIPERFECT CS-RINGS II Page 1 NONSINGULAR SEMIPERFECT CS-RINGS
II SK JAIN, P. KANWAR and SERGIO R. LOPEZ -PERMOUTH Abstract In this paper we …

L _1 identities and M is a left S-, right T-bimodule. For example any limited pp-ring is
isomorphic to a this type of matrix ring. Note that such a ring R need not be CS-ring in …

Abstract A module M is CS if every submodule of M is essential in a direct summand of M. In
this note we use the CS condition to provide conditions for semiperfect rings to be self …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

Rings for which every singular left module is injective, called SI-rings, were introduced and
studied by Goodearl [4]. He characterized such rings as those nonsingular ones for which …

An extension ring S of a ring T is called a left quotient ring of T if for any two elements ΛH= 0
and y of S there exists an element a of T such that ax^ rO and ay belongs to T. Let R be a …

Let R be a ring. A left R-module M is said to be min-injective if for any simple left ideal I. A
right R-module N is called min-flat if for any simple left ideal I. R is said to be a left min …