In this paper, we examine the invariants silp R and spli R that were defined for any ring R by
Gedrich and Gruenberg [9]. If the ring R is coherent on both sides, we show that silp R+ silp …

Relative homological groups over coherent rings Page 1 Quaestiones Mathematicae 35(2012),
331–352. c⃝ 2012 NISC Pty Ltd, www.nisc.co.za RELATIVE HOMOLOGICAL GROUPS OVER …

In this article, the notion of pure hereditary rings is introduced as a nontrivial generalization
of the notion of both pure semisimple rings and of hereditary rings. Some properties and …

A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

Restricted homological properties of modules Page 1 RESTRICTED HOMOLOGICAL
PROPERTIES OF MODULES DAVID A. HILL (Received 20 May 1971; revised 13 March 1972) …

This note is in a broad sense a continuation of [7]. If R is a ring (with identity) and its singular
ideal is zero then by results of Johnson and Wong any (left) injective hull h (R) of R admits a …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …

We study classes of modules over a commutative ring which allow to do homological
algebra relative to such a class. We classify those classes consisting of injective modules by …

Several authors have been interested in cotorsion theories. Among these theories we figure
the pairs $(\mathcal P_n,\mathcal P_n^{\perp}) $, where $\mathcal P_n $ designates the set …