Let R be a ring with identity element 1, and let S be a subring of R containing 1. We consider
R-modules on which 1 acts as the identity map, and we shall simultaneously regard such R …

Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …

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 …

We characterize a ring over which every left module of finite length has an injective hull of
finite length. Using this, we show that finite normalizing extensions of such a ring also have …

We present various approaches to J. Herzog's theory of generalized local cohomology and
explore its main aspects, eg,(non-) vanishing results as well as a general local duality …

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

Abstract Let R⊆ Q be rings such that the inclusion φ: R→ Q is an epimorphism in the
category of rings and Q is flat both as a right and as a left R-module. Assume that F. dim …

For a Noetherian local ring, the prime ideals in the singular locus completely determine the
category of finitely generated modules up to direct summands, extensions and syzygies …

This note presents the definitions of homological dimensions of bounded complexes of
modules as proposed by the author in [3]. Somewhat different definitions have been …

Let R be a commutative ring. We show that a finitely generated R-module M is reflexive
(equivalently, linearly compact) if and only if R/annR (M) is reflexive (equivalently, linearly …