Let $ R $ be a ring, and $ n $ a fixed nonnegative integer. An $ R $-module $ W $ is called $
L_ {n} $-injective if ${\rm Ext} _ {R}^{1}(M, W)= 0$ for any $ R $-module $ M $ with flat …

In this paper we define and study a new kind of dimension called, semisimple dimension,
that measures how far a module is from being semisimple. Like other kinds of dimensions …

The small finitistic dimension of a ring is determined as the supremum projective dimensions
among modules with finite projective resolutions. This paper seeks to establish that, for a …

Let R be a ring and C be a class of some finitely presented left R-modules. A left R-module
M is called C-injective if Ext ^1_R(C,M)=0 for every C∈C; a left R-module M is called C …

Recently, Costa [4] introduced the concept of n-coherent rings. In this note we shall give
some further properties of n-coherent rings. Let R be a ring and na nonnegative integer …

Let R be a ring. For two fixed positive integers m and n, a right R-module M is called (m, n)-
injective in case every right R-homomorphism from an n-generated submodule of Rm to M …

A ring is called right P-coherent if every principal right ideal is finitely presented. Let MR be a
right R-module. We study the P-coherence of the endomorphism ring S of MR. It is shown …

We introduce and study the c. Noetherian dimension of an R− module A, denoted by cn−
dim (A), which is the Noetherian dimension of the partially ordered set (briefly, poset) of …

Let R be a left coherent ring, FP—idRR the FP—injective dimension of RR and wD (R) the
weak global dimension of R. It is shown that 1) FP-idRR< n (n> 0) if and only if every flat …