Finitely generated mixed modules of Warfield type
Rendiconti del Seminario Matematico della Università di Padova, Tome 144 (2020), pp. 289-302.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

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 
@article{RSMUP_2020__144__289_0,
     author = {Zanardo, Paolo},
     title = {Finitely generated mixed modules of {Warfield} type},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {289--302},
     volume = {144},
     year = {2020},
     doi = {10.4171/rsmup/71},
     mrnumber = {4186461},
     zbl = {1476.13031},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/71/}
}
TY  - JOUR
AU  - Zanardo, Paolo
TI  - Finitely generated mixed modules of Warfield type
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2020
SP  - 289
EP  - 302
VL  - 144
UR  - http://www.numdam.org/articles/10.4171/rsmup/71/
DO  - 10.4171/rsmup/71
LA  - en
ID  - RSMUP_2020__144__289_0
ER  - 
%0 Journal Article
%A Zanardo, Paolo
%T Finitely generated mixed modules of Warfield type
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2020
%P 289-302
%V 144
%U http://www.numdam.org/articles/10.4171/rsmup/71/
%R 10.4171/rsmup/71
%G en
%F RSMUP_2020__144__289_0
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. http://www.numdam.org/articles/10.4171/rsmup/71/

Cité par Sources :