Torsion Z-module and Torsion-free Z-module

• Autorzy: Yuichi Futa , Hiroyuki Okazaki , Kazuhisa Nakasho , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

free Z-module; rank of Z-module; homomorphism of Z-module; linearly independent; linear combination

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2014
• Tom: 22
• Numer: 4
• Strony: 277-289

Daty

wydano

2014-12-01

otrzymano

2014-11-29

online

2014-12-31

Twórcy

autor

Yuichi Futa

• Japan Advanced Institute of Science and Technology Ishikawa, Japan

autor

Hiroyuki Okazaki

• Shinshu University Nagano, Japan

autor

Kazuhisa Nakasho

• Shinshu University Nagano, Japan

autor

Yasunari Shidama

• Shinshu University Nagano, Japan

Bibliografia

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Identyfikatory

DOI

10.2478/forma-2014-0028