Dual CS-Rickart Modules over Dedekind Domains

We study d-CS-Rickart modules (i.e. modules M such that for every endomorphism phi of M, the image of phi lies above a direct summand of M) over Dedekind domains. The structure of d-CS-Rickart modules over discrete valuation rings is fully determined. It is also shown that for a d-CS-Rickart R-module M over a nonlocal Dedekind domain R, the following assertions hold: The -primary component of is a direct summand of for any nonzero prime ideal of . MMR/() is an injective -module, where () is the torsion submodule of . MTMRTMMIf, moreover, M is a reduced R-module, then where P is the set of all nonzero prime ideals of R and is the -primary component of M for every .