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.
Cite this article
Paolo Zanardo, Finitely generated mixed modules of Warfield type. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 289–302DOI 10.4171/RSMUP/71