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  3. Formalized Mathematics
  4. Formalized Mathematics, 2013, Volume 21, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3696
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    Pole DCWartośćJęzyk
    dc.contributor.authorFuta, Yuichi-
    dc.contributor.authorOkazaki, Hiroyuki-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2015-12-09T20:40:19Z-
    dc.date.available2015-12-09T20:40:19Z-
    dc.date.issued2013-
    dc.identifier.citationFormalized Mathematics, Volume 21, Issue 4, 2013, Pages 273-282-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3696-
    dc.description.abstractIn 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.-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.subjectfree Z-module-
    dc.subjectsubmodule of free Z-module-
    dc.titleSubmodule of free Z-module-
    dc.typeArticle-
    dc.identifier.doi10.2478/forma-2013-0029-
    dc.description.AffiliationFuta Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, 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, 2013, Volume 21, Issue 4

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