Quotient Module of Z-module

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Okazaki, Hiroyuki	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-06T19:05:55Z	-
dc.date.available	2015-12-06T19:05:55Z	-
dc.date.issued	2012	-
dc.identifier.citation	Formalized Mathematics, Volume 20, Issue 3, 2012, Pages 205-214	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3644	-
dc.description.abstract	In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattices [14]. Some theorems in this article are described by translating theorems in [20] and [19] into theorems of Z-module.	-
dc.description.sponsorship	This work was supported by JSPS KAKENHI 22300285.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.title	Quotient Module of Z-module	-
dc.type	Article	-
dc.identifier.doi	10.2478/v10037-012-0024-y	-
dc.description.Affiliation	Futa Yuichi - Shinshu University, Nagano, Japan	-
dc.description.Affiliation	Okazaki Hiroyuki - Shinshu University, Nagano, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University, Nagano, Japan	-
dc.description.references	Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.	-
dc.description.references	Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.	-
dc.description.references	Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.	-
dc.description.references	Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.	-
dc.description.references	Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.	-
dc.description.references	Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.	-
dc.description.references	Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.	-
dc.description.references	Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.	-
dc.description.references	Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.	-
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	Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.	-
dc.description.references	Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.	-
dc.description.references	Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.	-
dc.description.references	Daniele Micciancio and Shafi Goldwasser. Complexity of lattice problems: A cryptographic perspective (the international series in engineering and computer science). 2002.	-
dc.description.references	Christoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.	-
dc.description.references	Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.	-
dc.description.references	Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.	-
dc.description.references	Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.	-
dc.description.references	Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.	-
dc.description.references	Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581-588, 1990.	-
dc.description.references	Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.	-
dc.description.references	Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.	-
dc.description.references	Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.	-
dc.description.references	Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.	-
dc.description.references	Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.	-
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