We investigate the structure of pure-syzygy modules in a pure-projective resolution of any
right R-module over an associative ring R with an identity element. We show that a right R …

Let A be a local ring that admits an exact pair x, y of zero divisors as defined by Henriques
and Şega. Assuming that this pair is orthogonal and that there exists a regular element on …

In this paper, we study the pure acyclic complexes of modules. We obtain several
characterizations of these complexes, extending results that are known for the pure acyclic …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …

Let $ R $ be a ring and $ E= E (R_R) $ its injective envelope. We show that if every simple
right $ R $-module embeds in $ R_R $ and every cyclic submodule of $ E_R $ is essentially …

In this note we prove that if $ R $ is a ring satisfying a polynomial identity and $ P $ is a
projective left $ R $-module such that $ P $ is finitely generated modulo the Jacobson …

We prove that every∑-pure-injective module over a serial ring is serial and every∑-pure-
injective faithful indecomposable module over a serial ring is∑-injective. Moreover, every …

We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a
direct sum of countably generated modules [2, Theorem l]. If any direct summand A of a …

We show that the class of rings with flat socles is closed under the formation of polynomial
extensions, direct products, and excellent extensions. We also point out that if a ring R can …

Recently KR Goodearl and D. Handelman [6] have studied simple regular rings from the
point of view of dimension-like functions. They have shown that there exists a unique …