JournalsrsmupVol. 144pp. 289–302

Finitely generated mixed modules of Warfield type

  • Paolo Zanardo

    Università degli Studi di Padova, Italy
Finitely generated mixed modules of Warfield type cover
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Abstract

Let RR be a local one-dimensional domain, with maximal ideal M\mathfrak M, which is not a valuation domain. We investigate the class of the finitely generated mixed RR-modules of Warfield type, so called since their construction goes back to R.B. Warfield. We prove that these RR-modules have local endomorphism rings, hence they are indecomposable. We examine the torsion part t(M)t(M) of a Warfield type module MM, investigating the natural property t(M)MMt(M) \subset \mathfrak M M. This property is related to b/ab/a being integral over RR, where aa and bb are elements of RR that define MM. We also investigate M/t(M)M/t(M) 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. 289–302

DOI 10.4171/RSMUP/71