Finitely generated mixed modules of Warfield type

Abstract

Let R be a local one-dimensional domain, with maximal ideal M, which is not a valuation domain. We investigate the class of the finitely generated mixed R-modules of Warfield type, so called since their construction goes back to R. B. Warfield. We prove that these R-modules have local endomorphism rings, hence they are indecomposable. We examine the torsion part t(M) of a Warfield type module M , investigating the natural property t(M) ⊂ MM . This property is related to b/a being integral over R, where a and b are elements of R that define M . We also investigate M/t(M) and determine its minimum number of generators. Mathematics Subject Classification (2010). 13G05, 13A15, 13A17.