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http://hdl.handle.net/11320/5489
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Pole DC | Wartość | Język |
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dc.contributor.author | Futa, Yuichi | - |
dc.contributor.author | Shidama, Yasunari | - |
dc.date.accessioned | 2017-05-16T09:30:37Z | - |
dc.date.available | 2017-05-16T09:30:37Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Formalized Mathematics, Volume 24, Issue 1, pp. 37-48 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/5489 | - |
dc.description.abstract | 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]. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.subject | divisible vector; divisible ℤ-module | - |
dc.subject | divisible ℤ-module | - |
dc.title | Divisible ℤ-modules | - |
dc.type | Article | - |
dc.identifier.doi | 10.1515/forma-2016-0004 | - |
dc.description.Affiliation | Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan | - |
dc.description.Affiliation | Shidama Yasunari - Shinshu University Nagano, Japan | - |
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dc.description.references | Wolfgang Ebeling. Lattices and Codes. Advanced Lectures in Mathematics. Springer Fachmedien Wiesbaden, 2013. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. ℤ-modules. Formalized Mathematics, 20(1):47-59, 2012. doi:10.2478/v10037-012-0007-z. | - |
dc.description.references | 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. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Free ℤ-module. Formalized Mathematics, 20(4):275-280, 2012. doi:10.2478/v10037-012-0033-x. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, Kazuhisa Nakasho, and Yasunari Shidama. Torsion ℤ-module and torsion-free Z-module. Formalized Mathematics, 22(4):277-289, 2014. doi:10.2478/forma-2014-0028. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, and Yasunari Shidama. Torsion part of ℤ-module. Formalized Mathematics, 23(4):297-307, 2015. doi:10.1515/forma-2015-0024. | - |
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Występuje w kolekcji(ach): | Formalized Mathematics, 2016, Volume 24, Issue 1 |
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