Torsion Z-module and Torsion-free Z-module
Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, Yasunari Shidama (2014)
Formalized Mathematics
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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].