Dolors Herbera (Universitat Aut\u00f2noma de Barcelona)<\/p>\n
Torsion free modules over commutative domains of Krull dimension 1 <\/em> Abstract: Let $R$ be a commutative domain. Let $\\mathcal F$ be the class of $R$-modules that are infinite direct sums of finitely generated torsion-free modules. In the talk we will discuss the question of whether $\\mathcal F$ is closed under direct summands.<\/p>\n If $R$ is local of Krull dimension 1, $\\mathcal F$ being closed under direct summands is equivalent to saying that any indecomposable, finitely generated torsion-free module has local endomorphism ring.<\/p>\n For the global case, we show also in the case of Krull dimension 1 that the property on $\\mathcal F$ is inherited by the localization at a maximal ideal. Moreover, there is an interesting relation between ranks of indecomposable modules over such localizations.<\/p>\n The machinery we use to prove these results was explained in Roman \u00c1lvarez’s talk, in the previous session of the seminar.<\/p>\n Time permitting, we will also discuss the property `being locally a direct summand’ versus `being a direct summand’ in the setting of our problem. The results we obtain allows us to give a complete answer to the initial problem in some particular cases.<\/p>\n The talk is based on a joint work with Roman \u00c1lvarez and Pavel P\u0159\u00edhoda.<\/p>\n","protected":false},"excerpt":{"rendered":" Dolors Herbera (Universitat Aut\u00f2noma de Barcelona) Torsion free modules over commutative domains of Krull dimension 1 Abstract: Let $R$ be a commutative domain. Let $\\mathcal F$ be the class of $R$-modules that are infinite direct sums of finitely generated torsion-free modules. In the talk we will discuss the question of whether $\\mathcal F$ is closed … <\/p>\n
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