P-adic decompositions over domains

Abstract.

We prove that in every domain R, there is a unique maximal submonoid T of R ^* = R\ {0} such that T-cotorsion R-modules admit P-adic decompositions.¶Furthermore, for a submonoid S of R ^*, the following are equivalent; (a) S is contained in T, (b) each element of S is contained in but a finite number of maximal ideals of R and each prime ideal of R which contains an element of S is contained in only one maximal ideal of R, (c) all S-cotorsion R-modules admit P-adic decompositions.