Torsion Z-module and Torsion-free Z-module

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Okazaki, Hiroyuki	-
dc.contributor.author	Nakasho, Kazuhisa	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-09T20:41:41Z	-
dc.date.available	2015-12-09T20:41:41Z	-
dc.date.issued	2014	-
dc.identifier.citation	Formalized Mathematics, Volume 22, Issue 4, 2014, Pages 277-289	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3724	-
dc.description.abstract	In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lov´asz) base reduction algorithm [20], cryptographic systems with lattice [21], and coding theory [11].	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	free Z-module	-
dc.subject	rank of Z-module	-
dc.subject	homomorphism of Z-module	-
dc.subject	linearly independent	-
dc.subject	linear combination	-
dc.title	Torsion Z-module and Torsion-free Z-module	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2014-0028	-
dc.description.Affiliation	Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan	-
dc.description.Affiliation	Okazaki Hiroyuki - Shinshu University Nagano, Japan	-
dc.description.Affiliation	Nakasho Kazuhisa - Shinshu University Nagano, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University Nagano, Japan	-
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