Divisible ℤ-modules

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

Abstrakty

EN

In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8].

Słowa kluczowe

EN

divisible vector; divisible ℤ-module

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2016
• Tom: 24
• Numer: 1
• Strony: 37-47

Daty

wydano

2016-03-01

otrzymano

2015-12-30

online

2016-08-19

Twórcy

autor

Yuichi Futa

• Japan Advanced Institute of Science and Technology Ishikawa, Japan

autor

Yasunari Shidama

• Shinshu University Nagano, Japan

Bibliografia

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• [10] Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Quotient module of ℤ-module. Formalized Mathematics, 20(3):205-214, 2012. doi:10.2478/v10037-012-0024-y.
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Identyfikatory

DOI

10.1515/forma-2016-0004