Let R be a ring. A left R-module M (respectively right R-module N) is called FI-injective
(respectively FI-flat) if Ext1 (G, M)= 0 (respectively Tor1 (N, G)= 0) for any FP-injective left R …

Let R be a left coherent ring, S any ring and RωS an (R, S)-bimodule. Suppose ωS has an
ultimately closed FP-injective resolution and RωS satisfies the conditions:(1) ωS is finitely …

In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial
generalization of flat (resp., injective) modules. We investigate the properties of these …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

In this paper we extend the notion of FP-injective modules to that of complexes and
characterize such complexes. We show that some characterizations similar to those for …

Let R be a ring. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …

A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A
left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1 (G, M)= 0 …

Let R be a regular ring of characteristic p> 0. In [4], Hochster showed that the category of
Lyubeznikʼs F R-modules has enough injectives, so that every F R-module has an injective …

NOTES ON FP-PROJECTIVE MODULES AND FP-INJECTIVE MODULES 1. Introduction
Throughout this paper, all rings are associative with id Page 1 February 17, 2006 17:49 …

An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential.
The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and …