In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

Let Λ and Γ be left and right noetherian rings and ΛU a Wakamatsu tilting module with Γ = End(ΛT ). We introduce a new definition of U -dominant dimensions and show that the U -dominant dimensions of ΛU and UΓ are identical. We characterize k-Gorenstein modules in terms of homological dimensions and the property of double homological functors preserving monomorphisms. We also study a generaliza...

This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...

Let a be an ideal of commutative Noetherian ring R with identity. We study finitely generated R-modules M whose a-finiteness and a-cohomological dimensions are equal. In particular, we examine relative analogues quasi-Buchsbaum, Buchsbaum surjective modules. reveal several interactions between these types modules that extend some the existing results in classical theory to one.

Let be a commutative ring with 1 and left unitary . In this paper, the generalizations for notions of compressible module retractable are given. An is termed to semi-essentially if can embedded in every non-zero semi-essential submodules. module, submodule an Some their advantages characterizations examples We also study relation between these classes some other modules.

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

Let R be local Noetherian ring of depth at least two. We prove that there are indecomposable R-modules which are free on the punctured spectrum of constant, arbitrarily large, rank.