In this article, we establish, as a generalization of a result on the classical homological
dimensions of commutative rings, an upper bound on the Gorenstein global dimension of …

R is called a right ${\Pi}-coherent $ ring in case every finitely generated torsion less right R-
module is finitely presented. In this paper, we define a dimension for rings, called ${\Pi} …

Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if
and only if Ext i (M, C)= 0 for all flat cotorsion right R-modules C and i≥ 1. Then we define …

New homotopy invariant finiteness conditions on modules over commutative rings are
introduced, and their properties are studied systematically. A number of finiteness results for …

We study partial homology and cohomology from the ring theoretic point of view via the
partial group algebra. In particular, we link the partial homology and cohomology of a group …

Let $\Lambda $ be a left and right Noetherian ring. First, for $ m, n\in\mathbb {N}\cup\{\infty\}
$, we give equivalent conditions for a given $\Lambda $-module to be $ n $-torsionfree and …

THE EXISTENCE OF FLAT COVERS flat, then <j> is called a flat cover of M if F' F —^— MF (b)
¡ \ F —^ M Page 1 proceedings OF THE AMERICAN MATHEMATICAL SOCIETY Volume 122 …

In this paper, we define a class of relative derived functors in terms of left or right weak flat
resolutions to compute the weak flat dimension of modules. Moreover, we investigate two …

Homological algebra modulo exact zero-divisors Page 1 Homological algebra modulo exact
zero-divisors Petter Andreas Bergh, Olgur Celikbas, and David A. Jorgensen Abstract We …

Let R be a ring, and M a bimodule over R. The trivial extension R x M is as abelian group
R@ M and the multiplication is given by (I, m)(r', m')=(rr', rm'+ mr'). Palmer and Roos give in …