Submodule of free Z-module

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

Abstrakty

EN

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems - LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are different.

Słowa kluczowe

EN

free Z-module; submodule of free Z-module

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2013
• Tom: 21
• Numer: 4
• Strony: 273-282

Daty

otrzymano

2013-12-31

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

10.2478/forma-2013-0029