The primary goal of this paper is to investigate the structure of irreducible monomorphisms to
and irreducible epimorphisms from finitely generated free modules over a noetherian local …

Let R be a local ring, and let M and N be finitely generated R-modules such that M has finite
complete intersection dimension. In this paper we define and study, under certain …

Let $ R $ be a commutative Noetherian ring with non-zero identity, $\mathfrak {a} $ an ideal
of $ R $, $ M $ a finitely generated $ R $--module, and $ X $ an arbitrary $ R $--module. In …

Let S be a regular local ring with residue field k and let M be a finitely generated S-module.
Suppose that f1,..., fc∈ S is a regular sequence that annihilates M, and let E be an exterior …

Let $(R,\mathfrak {m}) $ denote a local ring with $ E= E_R (k) $ the injective hull of $ k=
R/\mathfrak {m} $, its residue field. Let $ M $ denote a finitely generated $ R $-module. By …

Let ${P_R} $ be a projective module with trace ideal $ T $. An $ R $-module ${X_R} $ is $ T
$-accessible if $ XT= X.{\text {If}}{P_R} $ is finitely generated projective and $ C $ is the $ R …

We show that for a finitely generated module M over a complete intersection R, the
vanishing of for a certain number of consecutive values of i starting at n forces the projective …

Using the concept of prime submodule introduced by Raggi et. al. we extend the notion of
reduced rank to the module-theoretic context. We study the quotient category of $\sigma [M] …