Geodesic
Finitely generated mixed modules of Warfield type
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 289-302

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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.

Publié le :
DOI : 10.4171/rsmup/71
Classification : 13, 00 
Zanardo, Paolo. Finitely generated mixed modules of Warfield type. Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 289-302. doi: 10.4171/rsmup/71
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     title = {Finitely generated mixed modules of {Warfield} type},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {289--302},
     year = {2020},
     volume = {144},
     doi = {10.4171/rsmup/71},
     mrnumber = {4186461},
     zbl = {1476.13031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/rsmup/71/}
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