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Let be a local one-dimensional domain, with maximal ideal , which is not a valuation domain. We investigate the class of the finitely generated mixed -modules of Warfield type, so called since their construction goes back to R.B. Warfield. We prove that these -modules have local endomorphism rings, hence they are indecomposable. We examine the torsion part of a Warfield type module , investigating the natural property . This property is related to being integral over , where and are elements of that define . We also investigate and determine its minimum number of generators.
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Paolo Zanardo, Finitely generated mixed modules of Warfield type. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 289–302DOI 10.4171/RSMUP/71