The main purpose of this thesis is to investigate the notion of strongly noncosingular
modules. We call a right R-module M strongly noncosingular if for every nonzero right R …

Let R be a ring and M a fixed right R-module. A new characterization of M-flatness is given
by certain linear equations. For a left R-module F such that the canonical map M⊗ RF→ …

Motivated by a result of Mochizuki [Mochizuki, H.(1965). Finitistic global dimension for rings.
Pacific J. Math. 15 (1): 249–258] that, for a left perfect ring R with Jacobson radical if and …

A module M is called a CS-module if every submodule of M is essential in a direct summand
of M. It is shown that a ring R is semilocal if and only if every semiprimitive right R-module is …

It is shown that if M is a self-generator right R-module, then M is non-M-singular and CS iff M
is M-tight and End (MR) is a right PP ring. In particular, right nonsingular right CS-rings R are …

Let R be a ring. For a fixed positive integer n, R is said to be left n-semihereditary in case
every n-generated left ideal is projective. R is said to be weakly n-semihereditary if each n …

Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to
provide two new characterizations of coherent rings. The first of these characterizations …

Introduction. Let R be a ring (associative and with identity), M a quasiprojective left R-
module and S= End (RM). In [8] Wisbauer has given conditions under which S is a coherent …

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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 …