Publisher Summary This chapter describes the quasi-simple modules and weak transitivity.
If RVD be an R, D-bimodule, where D is a division ring R is a ring and RV is a uniform …

DEFINITION A. Let V be a left vector space over a division ring D and let R be a ring'of linear
transformations of V. Consider V as right R-module. Then R is weakly transitive provided …

In this short paper, the homological functors are used to show that a simple module is flat if
and only if it is injective. It is used to give a characterization of Von Neumann regular ring …

We define below a notion for modules which is dual to that of faithful, and a notion of “fully
divisible” which generalizes that of injectivity. We show that the bicommutator of a cofaithful …

1. Introduction and Statement of the Problem Recent important results in the area of quotient
rings (as in [U, 5, 6, 7, 13]) are based on certain interesting homological notions and results …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

In trying to extend the concept of torsion to rings more general than commutative integral
domains the first thing that we notice is that if the definition is carried over word for word …

1. If R is a ring and M is a (right) R-module such that MR= 0, then M is said to be quasi-
simple provided that (Ql) the endomorphism (module endomorphism) ring of the …

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

A commutative ring R with 1 over which the singular submodule is a direct summand for
every module, is a semihereditary ring with finitely many large ideals. A commutative semi …