In this work all rings are associative with unit unless otherwise stated, and all modules are
unital. If M is a left R-module, a flat preenvelope of M is a homomorphism M–“F, with F flat …

The injective hull of a module M can be characterized as a homomorphism f: M~ E (with E an
injective module) such that for each homomorphism g: M--* E'with E'injective, there exists a …

Introduction and summary. Of fundamental importance to the theory of ideals in commutative
rings satisfying the ascending chain condition for ideals has been the works of Noether [6] …

It is obvious that OF and Von Neumann regular rings have monomorphic flat envelopes. In
this paper we completely describe the structure, in terms of OF and Von Neumann regular …

A. Bak in [2] and CTC Wall in [8] have extended the concept of quadratic modules to
noncommutative rings. For modules over such rings we prove that under the assumptions M …

If R is a ring with identity, let N (R) denote the Jacobson radical of R. R is local if R/N (R) is
an artinian simple ring and∩ N (R) i= 0. It is known that if R is complete in the N (R)-adic …

We study noncommutative rings $ R $ having the property that there is no nonzero
homomorphism between injective hulls of nonisomorphic simple left $ R $-modules. For …

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) …

Let R be an arbitrary ring. A nonzero unital right R-module M is called a second module if M
and all its nonzero homomorphic images have the same annihilator in R. It is proved that if R …

This book is an account of a certain portion of noncommutative ring theory which originated
in the work of RE Johnson [113, 115], who introduced nonsingular rings, in 1951, and …