Divisible ℤ-modules

Pole DC	Wartość	Język
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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