On almost-free modules over complete discrete valuation rings
R. Göbel, B. Goldsmith (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Displaying similar documents to “Locally free modules”
On almost-free modules over complete discrete valuation rings
A note on basic free modules and the condition.
Marcelo, Agustín, Marcelo, Félix, Rodríguez, César (2006)
Portugaliae Mathematica. Nova Série
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On chains of free modules over valuation domains
Radoslav M. Dimitrić (1987)
Czechoslovak Mathematical Journal
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Torsion-free modules and syzygies.
Katz, D. (1994)
Mathematica Pannonica
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Chains of free modules and construction of -free modules
Radoslav Dimitrić (1987)
Rendiconti del Seminario Matematico della Università di Padova
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On a generalization of a Prüfer-Kaplansky-Procházka theorem
Luigi Salce (1989)
Commentationes Mathematicae Universitatis Carolinae
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Torsion Part of ℤ-module
Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2015)
Formalized Mathematics
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In this article, we formalize in Mizar [7] the definition of “torsion part” of ℤ-module and its properties. We show ℤ-module generated by the field of rational numbers as an example of torsion-free non free ℤ-modules. We also formalize the rank-nullity theorem over finite-rank free ℤ-modules (previously formalized in [1]). ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [23] and cryptographic systems with lattices [24].