In this note we shall use the same notations and terminologies as in [2]. In [2] we proved that,
if R is a weakly noetherian ring for which dim (mspec (R)) is finite, any nonfinitely generated …

Let R be a commutative Noetherian local ring and M, N be finitely generated R-modules. We
prove a number of results of the form: if Hom R (M, N) has some nice properties and Ext R …

It is proved that a module M over a commutative noetherian ring R is injective if Ext _ R^ i
((R/\mathfrak p) _\mathfrak p, M)= 0 Ext R i ((R/p) p, M)= 0 holds for every i\geqslant 1 i⩾ 1 …

Let R be a noetherian commutative local ring, and M, N be finitely generated R-modules.
Then a generalized form of Serre's Vanishing conjecture can be stated as follows: if then …

Cohen–Macaulayness of trivial extensions Page 1 Journal of Algebra and Its Applications Vol.
17, No. 1 (2018) 1850008 (15 pages) c© World Scientific Publishing Company DOI …

We present a classification of those finite length modules X over a ring A that are isomorphic
to every module Y of the same length such that Ker (Hom A (−, X))= Ker (Hom A (−, Y)), that …

Let R be a commutative ring with 1, and let M be a (left) unitary R-module, let S= End (M) be
the ring of R-endomorphisms of M. In this paper we look at some ring theoretic and module …

Let R be a Noetherian homogeneous (eg standard graded) ring with local Artinian base ring
(in degree 0), and let M and N be two finitely generated graded R-modules. We give various …

A module is said to be extending, if every closed (ie complement) submodule is a direct
summand. This property is usually denoted by (Q). It is, obviously, equivalent to the …

The Ext-Groups of Generalized Macaulay–Northcott Modules* Page 1 Vietnam Journal of
Mathematics 32:2 (2004) 161–169 9LHWQDP -RXUQDO RI 0$7+(0$7,&6 9$67 The Ext-Groups …