A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

This paper unifies several generalizations of coherent rings in one notion. Namely, we
introduce nX-coherent rings, where X is a class of modules and n is a positive integer, as …

A ring R is called right PCI if every proper cyclic right R-module is injective, ie if C is a cyclic
right R-module then CR≅ RR or CR is injective. By [2] and [3], if R is a non-artinian right PCI …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

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 …

By a well-known result of Osofsky [6, Theorem] a ring R is semisimple (ie R is right artinian
and the Jacobson radical of R is zero) if and only if every cyclic right R-module is injective …

Let M be a right R-module with S= End (MR). Given two cardinal numbers α and β and a row-
finite matrix A∈ RFM β× α (S), SM is called injective relative to A if every left S …

It is proved that A is a right distributive ring if and only if all quasiinjective right A-modules are
Bezout left modules over their endomorphism rings if and only if for any quasiinjective right A …

A ring R is said to be left pure-hereditary (resp. RD-hereditary) if every left ideal of R is pure-
projective (resp. RD-projective). In this paper, some properties and examples of these rings …