Isomorphism Theorem on Vector Spaces over a Ring

Pole DC	Wartość	Język
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2018-02-08T08:13:51Z	-
dc.date.available	2018-02-08T08:13:51Z	-
dc.date.issued	2017	-
dc.identifier.citation	Formalized Mathematics, Volume 25, Issue 3, Pages 171–178	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/6291	-
dc.description.abstract	SummaryIn this article, we formalize in the Mizar system [1, 4] some properties of vector spaces over a ring. We formally prove the first isomorphism theorem of vector spaces over a ring. We also formalize the product space of vector spaces. ℤ-modules are useful for lattice problems such as LLL (Lenstra, Lenstra and Lovász) [5] base reduction algorithm and cryptographic systems [6, 2].	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	isomorphism theorem	-
dc.subject	vector space	-
dc.title	Isomorphism Theorem on Vector Spaces over a Ring	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2017-0016	-
dc.description.Affiliation	Futa Yuichi - Tokyo University of Technology, Tokyo, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University, Nagano, Japan	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.	-
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. Submodule of free ℤ-module. Formalized Mathematics, 21(4):273–282, 2013. doi:10.2478/forma-2013-0029.	-
dc.description.references	Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.	-
dc.description.references	A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen, 261(4):515–534, 1982. doi:10.1007/BF01457454.	-
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	Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31–40, 2012. doi:10.2478/v10037-012-0005-1.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	25	-
dc.description.issue	3	-
dc.description.firstpage	171	-
dc.description.lastpage	178	-
dc.identifier.citation2	Formalized Mathematics	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2017, Volume 25, Issue 3

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