Affiliation:
1. Japan Advanced Institute of Science and Technology Ishikawa, Japan
2. Shinshu University Nagano, Japan
Abstract
Summary
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].
Subject
Applied Mathematics,Computational Mathematics
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Lattice of ℤ-module;Formalized Mathematics;2016-03-01
2. Divisible ℤ-modules;Formalized Mathematics;2016-03-01
3. Torsion Part of ℤ-module;Formalized Mathematics;2015-12-01