Torsion Part of ℤ-module

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

Abstrakty

EN

In this article, we formalize in Mizar [7] the definition of “torsion part” of ℤ-module and its properties. We show ℤ-module generated by the field of rational numbers as an example of torsion-free non free ℤ-modules. We also formalize the rank-nullity theorem over finite-rank free ℤ-modules (previously formalized in [1]). ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [23] and cryptographic systems with lattices [24].

Słowa kluczowe

EN

torsion part of ℤ-module; torsion-free non free ℤ-module

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 15A03: Vector spaces, linear dependence, rank
• 13C12: Torsion modules and ideals

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 4
• Strony: 297-307

Daty

wydano

2015-12-01

otrzymano

2015-08-14

online

2016-03-25

Twórcy

autor

Yuichi Futa

• Japan Advanced Institute of Science and Technology, Ishikawa, Japan

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

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Identyfikatory

DOI

10.1515/forma-2015-0024

bwmeta1.id-class.MML

ZMODUL07