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 …

Balanced ring is defined and related to Thrall's QF-1 rings. Several theorems are obtained
which show that balanced rings enjoy strong homological and chain conditions. The …

Abstract A right R–module E over a ring R is said to be maximally injective in case for any
maximal right ideal m of R, every R–homomorphism f: m→ E can be extended to an R …

Tachikawa showed that a left perfect ring R is an injective cogenerator in the category of all
right R-modules iff there holds:(right FPF) every finitely generated faithful right module …

R (finitely cogenerated) injective cogenerator in the category of right R-modules. The ring R
is a QF-ring if it is right PF and right (or left) artinian, and in this case R is two-sided PF and …

1* Introduction* An associative ring R is called a left (F) PF ring if every (finitely generated)
faithful module generates the category of left ϋ?-modules. Azumaya [1], Osofsky [7], and …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

(1) R is right PF.(2) R is an injective cogenerator in 51R.(3) E (RR) is torsionless and R is an
S-ring.(4) R is a cogenerator in vdR and is a right S-ring. In this paper we shall be concerned …

Utilizing a matrix representation of semiperfect rings by a family of bimodules over local
rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic …

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