A GENERALIZATION OF n-TORSIONFREE MODULES 1. Introduction In the late 1960s,
Auslander and Bridger [2] constructed the notion of Page 1 A GENERALIZATION OF n-TORSIONFREE …

This paper gives a new approximation theory for finitely generated modules over
commutative Noetherian rings, which unifies two famous approximation theorems; one is …

Goldman [3] has introduced the notion of the length of a module with respect to a torsion
theory and has studied finitely-generated modules over left noetherian rings which have …

We show how a number of well—known results follow from a characterization of torsion—
free modules. In this note we bring to light a result which seems to be lying beneath the …

If R is a commutative Noetherian ring then the Forster-Swan Theorem and the stable version
of that result due to Eisenbud and Evans give information concerning the number of …

The well-known Forster-Swan theorem gives a bound bn the number of generators of a
finitely generated module over a suitable ring in terms of local data. In section 2 of this …

Let R be a reduced one-dimensional Noetherian ring with finite integral closure R, and
conductor C and let@(A) denote the set of isomorphism classes of finitely generated …

In this note we shall use the same notations and terminologies as in [2]. In [2] we proved that,
if R is a weakly noetherian ring for which dim (mspec (R)) is finite, any nonfinitely generated …

Recently Takahashi established a new approximation theory for finitely generated modules
over commutative Noetherian rings, which unifies the spherical approximation theorem due …

The Eakin-Nagata theorem says that if $ T $ is a commutative Noetherian ring which is
finitely generated as a module over a subring $ R $, then $ R $ is also Noetherian. This …