The aim of this paper is twofold. Firstly, to give short proofs of the celebrated results of Rudd
(1970), De Marco (1972), Brookshear (1977), Neville (1990), and Vechtomov (1996) with the …

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-
injective, if Ext R 1 (C, M)= 0 for each C∈ C. A right R-module M is called C-flat, if Tor 1 R …

A module M over a ring R is said to be purely Rickart if the right annihilator in M of each
endomorphism ring of a module M is a pure submodule of M. Purely Rickart module is a …

Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of
S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator ann M n …

Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if
every n-generated submodule of M is finitely presented (resp. projective). We investigate the …

Let R be a ring, let I be an ideal of R, and let n be a fixed positive integer. We define and
study In-injective modules and In-flat modules. Moreover, we define and study left In …

Let R be a ring. A left R-module M is called a cp module if every cyclic submodule of M is
projective. This notion is a generalization of left pp rings in the general module theoretic …

Let m and n be fixed positive integers. R is called a right (m, n)-injective ring if every right R-
homomorphism from an n-generated submodule of the right R-module R m to R extends to …

Let $ R $ be a ring and $ n $ a fixed positive integer. A right $ R $-module $ M $ is called
strongly $ J $-$ n $-injective if every $ R $-homomorphism from an $ n $-generated small …

On Π- coherence of rings Page 1 Hacettepe Journal of Mathematics and Statistics Volume
46 (5) (2017), 875 – 886 On Π- coherence of rings Zhu Zhanmin∗ Abstract Let n be a fixed …