We show that the cosupport of a commutative noetherian ring is precisely the set of primes
appearing in a minimal pure-injective resolution of the ring. As an application of this, we …

A module over a ring $ R $ is pure projective provided it is isomorphic to a direct summand
of a direct sum of finitely presented modules. We develop tools for the classification of pure …

Abstract The well-known Forster-Swan theorem, and the stable version of this result given by
Eisenbud and Evans, give a bound on the number of generators of a module over a …

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 Forster-Swan Theorem gives an upper bound on the number of generators of a module
over a commutative ring in terms of local data. Stafford showed that this theorem could be …

Let R be a reduced commutative Noetherian ring. We provide conditions equivalent to
isomorphism for completely decomposable finitely generated modules over R. We show …

Those modules over a commutative Noetherian ring which are finitely generated (and
therefore automatically finitely presented) have especially pleasant properties. For example …

Examples are given to show that the support of a complex of modules over a commutative
noetherian ring may not be read off the minimal semi-injective resolution of the complex. The …

In this note we show that a countable injective module is $\sum $-injective and consequently
a ring $ R $ is left noetherian if the category of left $ R $-modules has a countable injective …

In the derived category of modules over a commutative noetherian ring a complex $ G $ is
said to generate a complex $ X $ if the latter can be obtained from the former by taking …