There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

Contents. 1. Introduction and Notation; 2. A Jacobian Criterion for Separability; 3. A Jacobian
Criterion for Extension of Derivations; 4. Explicit Formulas for the Separability Idempotent; …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

If R is a ring of coefficients and G a finite group, then a flat RG-module which is projective as
an R-module is necessarily projective as an RG-module. More generally, if H is a subgroup …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

In this paper, we use the notion of strict Mittag–Leffler modules, in order to study the flat
length of injective modules over a ring R. We show that the supremum of these flat lengths is …

Let R be a left and right ℵ0-Noetherian ring. We show that if all projective left and all
projective right R-modules have finite injective dimension, then all injective left and all …

ON REGULARITY OF RINGS 1 Page 1 ON REGULARITY OF RINGS 1 Jianlong Chen Department
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …

0. Introduction. We begin here an inquiry into the nature of flat ideals in a commutative ring
A, with particular emphasis on questions of divisibility and finite generation As the main …

UPPER BOUNDS ON HOMOLOGICAL DIMENSIONS Page 1 UPPER BOUNDS ON
HOMOLOGICAL DIMENSIONS BL OSOFSKY The homological dimension of a module MR is …