2026-04-17T05:53:19Zhttps://recercat.cat/oai/request
oai:recercat.cat:2072/4893092026-03-10T09:00:10Zcom_2072_199267com_2072_4427col_2072_201036
RECERCAT author Alvarez, R. author Herbera, Dolors author Príhoda, P. 2026-03-10T08:36:40Z 2026-03-10T08:36:40Z 2025-05-21 https://hdl.handle.net/2072/489309 10.4171/rmi/1564 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. eng Attribution 4.0 International Torsion-free modules over commutative domains of Krull dimension one info:eu-repo/semantics/article URL https://recercat.cat/bitstream/2072/489309/1/Torsion-free%20modules%20over%20commutative%20domains%20of%20Krull%20dimension%20one.pdf File MD5 624cf57ea2a054a7bc56fd9fac5bd61a 799241 application/pdf Torsion-free modules over commutative domains of Krull dimension one.pdf URL https://recercat.cat/bitstream/2072/489309/3/Torsion-free%20modules%20over%20commutative%20domains%20of%20Krull%20dimension%20one.pdf.txt File MD5 56ae520b89372f9ff3374d0a9198fcb8 171683 text/plain Torsion-free modules over commutative domains of Krull dimension one.pdf.txt