On primes dual to associated primes for cotorsion modules

Abstract

Using the theory of flat covers, we introduce a set of primes dual to the set of associated primes. It turns out that this set has properties similar (or rather dual) to those of the set of associated primes. With the aid of this set of primes, we obtain a necessary and sufficient condition for a cotorsion module M, over a ring whose injective hull is flat, to have a nonzero injective cover.