In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lov´asz) base reduction algorithm [20], cryptographic systems with lattice [21], and coding theory [11].
@article{bwmeta1.element.doi-10_2478_forma-2014-0028,
author = {Yuichi Futa and Hiroyuki Okazaki and Kazuhisa Nakasho and Yasunari Shidama},
title = {Torsion Z-module and Torsion-free Z-module},
journal = {Formalized Mathematics},
volume = {22},
year = {2014},
pages = {277-289},
zbl = {1316.13012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0028}
}
Yuichi Futa; Hiroyuki Okazaki; Kazuhisa Nakasho; Yasunari Shidama. Torsion Z-module and Torsion-free Z-module. Formalized Mathematics, Tome 22 (2014) pp. 277-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0028/
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