In this paper we begin to study the algebra structures that may be given to finite free
resolutions of cyclic modules over a local noetherian ring. Using these algebra structures …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

In this paper, apart from section three, all the rings considered are assumed to be right and
left noetherian. We follow the notation of [3]. In [3], Goldie has given a method for …

Introduction. The aim of this paper is to show the relevance of a class of commutative
noetherian rings to the study of reflexive nmod-ules. They include integrally closed domains …

In this paper we prove that all finitely generated projective modules over a polynomial ring k
[T~..... T,] are free when k is a field, or more generally a principal ideal domain. This settles …

A characterization is given of those Noetherian rings $ R $ such that whenever $ R $ is
ideally closed ($\equiv $ cyclically pure) in an extension algebra $ S $, then $ R $ is pure in …

THROUGHOUT this paper'module'will mean'unitary left B-module', where R is an
associative ring with 1. Morphisms will be written acting on the side opposite scalar …

Let $ A $ be a regular local ring of positive characteristic. This paper is concerned with the
local cohomology modules of $ A $ itself, but with respect to an arbitrary ideal of $ A $. The …

Given two homomorphisms of rings j1: R1→ R'and j2: R2→ R'we may construct a new ring R
called the pullback of R1 and R2 over R', together with homomorphisms i1: R→ R1 and i2 …

It is easy to see that the point defined by F (xo, x1)= 0, x2= Xn= 0 has degree p and lies on
Sn. Let x be any point on Xn. Let r be the largest integer such that x lies in the affine open …