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.

We prove that if $R$ is a commutative Noetherian ring, then every countably generated flat $R$-module quite flat, i.e., direct summand of transfinite extension localizations in countable multiplicative subsets. also show the spectrum cardinality less than $\kappa$, where $\kappa$ an uncountable regular cardinal, modules with generators. This provides alternative proof fact over ring spectrum, a...

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.

In 1995, Faith and Menal have established the V-ring theorem which gives a characterization of a V-ring. In this paper, we generalize this theorem to V-modules and consider some applications for Noetherian self-cogenerators.

This is an exposition of Goldie’s theorem with a section on Ore localization and with an application to defining ranks for finitely generated modules over non–commutative noetherian rings.

In this note, it is proved that over a commutative noetherian henselian non-Gorenstein local ring there are infinitely many isomorphism classes of indecomposable totally reflexive modules, if there is a nonfree cyclic totally reflexive module.