Let (R,m) be a commutative Noetherian local ring with m = (0). We give a condition for R to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of projective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over R is not necessarily a...

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...

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module 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.

In the theory of modules over commutative rings there are several possibilities of defining associated prime ideals. The usual definition of an associated prime ideal p for a module M is that p is the annihilator of an element of M . In [2] §1 exercise 17 a generalization of this notion is given. p is called weakly associated (faiblement associé) to M if p is minimal in the set of the prime ide...

For any commutative ring $A$ we introduce a generalization of $S$--noetherian rings using here\-ditary torsion theory $\sigma$ instead multiplicatively closed subset $S\subseteq{A}$. It is proved that totally noetherian w.r.t. local property, and if w.r.t $\sigma$, then finite type.