We revisit two questions concerning the existence of a single test module by comparing
them with similar questions (see Theorem 3.3). As a corollary, we identify domains over …

The purpose of this expository note is to establish the fact mentioned in the title. While this is
not difficult and requires no new ideas, it seems worth doing, as such a simple …

Let $ R $ be a commutative noetherian local ring with identity. Modules over $ R $ will be
assumed to be finitely generated and unitary. A nonzero $ R $-module $ M $ is said to be a …

A (right $ R $-) module $ N $ is said to be a Whitehead test module for projectivity (shortly: a
p-test module) provided for each module $ M $, $ Ext_R (M, N)= 0$ implies $ M $ is …

We prove that if a local ring admits a pd-test module of finite complete intersection
dimension, then it is a complete intersection ring. This answers, positively, a question …

If R is an integral domain, let be the class of torsion free completely decomposable R-
modules of finite rank. Denote by the class of those torsion-free R-modules A such that A is …

We introduce the notion of strong test module and show that a large number of such
modules appear in the tight closure theory of complete domains: the test ideal (this has …

THE EXISTENCE OF DUAL MODULES JkA + Q Bn = Q (JkA + B„) = JkA + Bn(k) Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 55, Number 2, March …

We extend the notion of test module filtration introduced by Blickle for Cartier modules. We
then show that this naturally defines a filtration on unit F-modules and prove that this filtration …

Our main purpose is to characterize the class of almost perfect domains (introduced by
Bazzoni and Salce [S. Bazzoni, L. Salce, Almost perfect domains, Colloq. Math. 95 (2003) …