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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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1898-9934
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Volume 21, Issue 4

Issues

Submodule of free Z-module

Yuichi Futa / Hiroyuki Okazaki / Yasunari Shidama
Published Online: 2013-12-27 | DOI: https://doi.org/10.2478/forma-2013-0029

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.

Keywords: free Z-module; submodule of free Z-module

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About the article

Received: 2013-12-31

Published Online: 2013-12-27

Published in Print: 2013-12-01


Citation Information: Formalized Mathematics, Volume 21, Issue 4, Pages 273–282, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/forma-2013-0029.

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© by Yuichi Futa. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0) BY-SA 3.0

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[1]
Yuichi Futa and Yasunari Shidama
Formalized Mathematics, 2017, Volume 25, Number 3

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