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  3. Formalized Mathematics
  4. Formalized Mathematics, 2012, Volume 20, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3653
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    Pole DCWartośćJęzyk
    dc.contributor.authorFuta, Yuichi-
    dc.contributor.authorOkazaki, Hiroyuki-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2015-12-06T19:06:09Z-
    dc.date.available2015-12-06T19:06:09Z-
    dc.date.issued2012-
    dc.identifier.citationFormalized Mathematics, Volume 20, Issue 4, 2012, Pages 275-280-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3653-
    dc.description.abstractIn this article we formalize a free ℤ-module and its rank. We formally prove that for a free finite rank ℤ-module V , the number of elements in its basis, that is a rank of the ℤ-module, is constant regardless of the selection of its basis. ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [15]. Some theorems in this article are described by translating theorems in [21] and [8] into theorems of Z-module.-
    dc.description.sponsorshipThis work was supported by JSPS KAKENHI 21240001 and 22300285.-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleFree Z-module-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-012-0033-x-
    dc.description.AffiliationFuta Yuichi - Shinshu University, Nagano, Japan-
    dc.description.AffiliationOkazaki Hiroyuki - Shinshu University, Nagano, Japan-
    dc.description.AffiliationShidama Yasunari - Shinshu University, Nagano, Japan-
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    Występuje w kolekcji(ach):Formalized Mathematics, 2012, Volume 20, Issue 4

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