Polyserial modules over valuation domains

L. Fuchs; L. Salce

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Some properties of Butler modules over valuation domains

Elisabetta Monari Martinez (1991)

Rendiconti del Seminario Matematico della Università di Padova

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Local height functions and the Mordell-Weil theorem for Drinfeld modules

Bjorn Poonen (1995)

Compositio Mathematica

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Classes of modules related to Serre subcategories.

Crivei, Septimiu, Crivei, Iuliu (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Divisible ℤ-modules

Yuichi Futa, Yasunari Shidama (2016)

Formalized Mathematics

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In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8]. ...