Some properties of Butler modules over valuation domains
Elisabetta Monari Martinez (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Elisabetta Monari Martinez (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Bjorn Poonen (1995)
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Yuichi Futa, Yasunari Shidama (2016)
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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]. ...
Gabriella D'Este, Dieter Happel (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Alberto Facchini (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Kamal, Mahmoud Ahmed (1994)
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Mark L. Teply, Blas Torrecillas (1993)
Czechoslovak Mathematical Journal
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Wang, Yongduo (2005)
International Journal of Mathematics and Mathematical Sciences
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