It is shown that a ring R is semiprime right Goldie if and only if R is right nonsingular and
every nonsingular right R-module M has a direct decomposition M= I⊕ N, where I is injective …

NONSINGULAR EXTENDING MODULES Page 1 NONSINGULAR EXTENDING MODULES
PATRICK F. SMITH ABSTRACT. In this paper, it is shown that if R is a semiprime right Goldie …

Throughout this note, all rings are assumed to be associative and to have an identity.
Likewise, all modules are supposed to be unitary. A right R-module MR is called a CS …

We prove that if R is an idempotent reflexive left Goldie ring whose simple singular left R-
modules are GP-injective, then R is a finite product of simple left Goldie rings. As a …

Let R be a semiprime, right Goldie ring, with semisimple Artinian right quo-tient ring Q (R). If
M is a right R-module, then the Goldie rank of M, written Grkº M, or Grk M if the context is …

The notation in this paper will be standard and it may be found in [3], for example. In
particular, the notation A⊂′ B stands for the statement “A is an essential submodule of B” …

A ring A is a right automorphism-invariant right non-singular ring if and only if A= S× T,
where S a right self-injective regular ring and T is a strongly regular ring which contains all …

We say that an R-module M satisfies epi-ACC on submodules if in every ascending chain of
submodules of M, except probably a finite number, each module in chain is a homomorphic …

A right R-module M is called a Goldie module if it has finite Goldie dimension and satisfies
the ACC for M-annihilator submodules of M. In this paper, we study the class of prime Goldie …

For an R-module M, projective in σ [M] and satisfying ascending chain condition on left
annihilators, the authors introduce the concept of Goldie module. The authors also use the …