Let $ k $ be a field with characteristic zero, $ R $ be the ring $ k [x_1,\cdots, x_n] $ and $ I $
be a monomial ideal of $ R $. We study the Artinian local algebra $ R/I $ when considered …

Let $(R, m) $ be a two-dimensional regular local ring with infinite residue field. For a finitely
generated, torsion-free $ R $-module $ A $, write $ A_ {n} $ for the $ n $ th symmetric power …

We investigate Matlis duals of local cohomology modules and prove that, in general, their
zeroth Bass number with respect to the zero ideal is not finite. We also prove that, somewhat …

Let $\Lambda $ be a module-finite algebra over a commutative noetherian ring $ R $ of Krull
dimension 1. We determine when a collection of finitely generated modules over the …

Let R be an associated ring not necessarily with identity, M a left R-module having the
property (F), and (S,≤) a strictly totally ordered monoid which is also artinian and finitely …

Let R be a ring. Any R-module M which is Artinian or Noetherian can be written as the direct
sum of a finite number of indecomposable R-modules. The theorem of Krull–Remak …

We are interested in constructions of modules occurring in Grothendieck or Matlis duality
theory, for example modules with zero dimeiisional support over a local ring, injective hulls …

In this paper, we explore the relation between small cofinite irreducibles and cyclic
submodules in the dual. As an application, we show that an Artinian module over a …

This paper explicitly determines the core of a torsion-free, integrally closed module over a
two-dimensional regular local ring. It is analogous to a result of Huneke and Swanson which …

For a Noetherian local ring (R, m) with p∈ Spec (R), we denote the R-injective hull of R/p by
ER (R/p). We show that it has an Rˆp-module structure, and there is an isomorphism ER …