In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattices [14]. Some theorems in this article are described by translating theorems in [20] and [19] into theorems of Z-module.
@article{bwmeta1.element.doi-10_2478_v10037-012-0024-y,
author = {Yuichi Futa and Hiroyuki Okazaki and Yasunari Shidama},
title = {Quotient Module of Z-module},
journal = {Formalized Mathematics},
volume = {20},
year = {2012},
pages = {205-214},
zbl = {06213839},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0024-y}
}
Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama. Quotient Module of Z-module. Formalized Mathematics, Tome 20 (2012) pp. 205-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-012-0024-y/
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