Divisible ℤ-modules

Clicks: 187
ID: 97384
2016
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Abstract
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].
Reference Key
yuichi2016divisibleformalized Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Yuichi, Futa;Yasunari, Shidama;
Journal formalized mathematics
Year 2016
DOI
DOI not found
URL
http://www.degruyter.com/view/j/forma.2016.24.issue-1/forma-2016-0004/forma-2016-0004.xml?format=INT
Keywords
Medicine Technology Science mathematics nuclear and particle physics. atomic energy. radioactivity

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