2026-04-14T08:27:23Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4893092026-03-10T09:00:10Zcom_2072_199267com_2072_4427col_2072_201036

Torsion-free modules over commutative domains of Krull dimension one Alvarez, R. Herbera, Dolors Príhoda, P. torsion-free modules h-local domain infinite direct sum decomposition 2-generated ideals stable categories relatively big projective modules 51 Let R be a domain of Krull dimension one. We study when the class F of modules over R that are arbitrary direct sums of finitely generated torsion-free modules is closed under direct summands. If R is local, we show that F is closed under direct summands if and only if any indecomposable, finitely generated, torsion-free module has local endomorphism ring. If, in addition, R is noetherian, this is equivalent to saying that the normalization of R is a local ring. If R is an h-local domain of Krull dimension 1 and F-R is closed under direct summands, then the property is inherited by the localizations of R at maximal ideals. Moreover, any localization of R at a maximal ideal, except maybe one, satisfies that any finitely generated ideal is 2-generated. The converse is true when the domain R is, in addition, integrally closed, or noetherian semilocal, or noetherian with module-finite normalization. Finally, over a commutative domain of finite character and with no restriction on the Krull dimension, we show that the isomorphism classes of countably generated modules in F are determined by their genus. The research of the first author was supported by the pre-doctoral grant 2021FIB00913 of the Generalitat de Catalunya.The second author was supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). The first and second authors were partially supported by the projects MIMECO PID2020-113047GB-I00 and PID2023-147110NB-I00 financed by the Spanish Government, and by Laboratori d'Interaccions entre Geometria, & Agrave;lgebrai Topologia (LIGAT) with reference number 2021 SGR 01015 financed by the Generalitat de Catalunya.The third author was supported by Czech Science Foundation grant GACR 23-05148S info:eu-repo/semantics/publishedVersion 2025-05-21 info:eu-repo/semantics/article https://hdl.handle.net/2072/489309 10.4171/rmi/1564 eng Revista Matematica Iberoamericana Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess 64 p. application/pdf EMS Press RECERCAT (Dipòsit de la Recerca de Catalunya)