Submodule of free Z-module

Yuichi Futa; Hiroyuki Okazaki; Yasunari Shidama

doi:10.2478/forma-2013-0029

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Submodule of free Z-module

Formalized Mathematics

Volume 21 (2013): Issue 4 (December 2013)

By: Yuichi Futa, Hiroyuki Okazaki and Yasunari Shidama

Open Access

|Dec 2013

Abstract

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.

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2013-0029 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 273 - 282

Submitted on: Dec 31, 2013

Published on: Dec 27, 2013

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

free Z-module,

submodule of free Z-module

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2013 Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 21 (2013): Issue 4 (December 2013)