In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are different.
@article{bwmeta1.element.doi-10_2478_forma-2013-0029,
author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama},
title = {Submodule of free Z-module},
journal = {Formalized Mathematics},
volume = {21},
year = {2013},
pages = {273-282},
zbl = {1298.13013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0029}
}
Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama. Submodule of free Z-module. Formalized Mathematics, Tome 21 (2013) pp. 273-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0029/
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