On w∞ -Warfield Cotorsion Modules and Krull Domains

Abstract

Let [Formula: see text] be a commutative domain with 1 and [Formula: see text] [Formula: see text] its field of quotients. In this note an [Formula: see text]-module [Formula: see text] is called [Formula: see text]-Warfield cotorsion if [Formula: see text], where [Formula: see text] denotes the class of all Warfield cotorsion [Formula: see text]-modules and [Formula: see text] the class of all [Formula: see text]-projective [Formula: see text]-modules. It is shown that [Formula: see text] is a PVMD if and only if all [Formula: see text]-cotorsion [Formula: see text]-modules are [Formula: see text]-Warfield cotorsion, and that [Formula: see text] is a Krull domain if and only if every [Formula: see text]-Matlis cotorsion strong [Formula: see text]-module over [Formula: see text] is a [Formula: see text]-Warfield cotorsion [Formula: see text]-module.