Torsion Part of ℤ-module

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	pl
dc.contributor.author	Okazaki, Hiroyuki	pl
dc.contributor.author	Shidama, Yasunari	pl
dc.date.accessioned	2016-12-16T10:30:40Z	-
dc.date.available	2016-12-16T10:30:40Z	-
dc.date.issued	2015	pl
dc.identifier.citation	Formalized Mathematics, Volume 23, Issue 4, 297–307	pl
dc.identifier.issn	1426-2630	pl
dc.identifier.issn	1898-9934	pl
dc.identifier.uri	http://hdl.handle.net/11320/4904	-
dc.description.abstract	In this article, we formalize in Mizar [7] the definition of “torsion part” of ℤ-module and its properties. We show ℤ-module generated by the field of rational numbers as an example of torsion-free non free ℤ-modules. We also formalize the rank-nullity theorem over finite-rank free ℤ-modules (previously formalized in [1]). ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [23] and cryptographic systems with lattices [24].	pl
dc.language.iso	en	pl
dc.publisher	De Gruyter Open	pl
dc.subject	torsion part of ℤ-module	pl
dc.subject	torsion-free non free ℤ-module	pl
dc.title	Torsion Part of ℤ-module	pl
dc.type	Article	pl
dc.identifier.doi	10.1515/forma-2015-0024	pl
dc.description.Affiliation	Yuichi Futa - Japan Advanced Institute of Science and Technology, Ishikawa, Japan	pl
dc.description.Affiliation	Hiroyuki Okazaki - Shinshu University, Nagano, Japan	pl
dc.description.Affiliation	Yasunari Shidama - Shinshu University, Nagano, Japan	pl
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