On Roots of Polynomials and Algebraically Closed Fields

Pole DC	Wartość	Język
dc.contributor.author	Schwarzweller, Christoph	-
dc.date.accessioned	2018-02-08T08:13:52Z	-
dc.date.available	2018-02-08T08:13:52Z	-
dc.date.issued	2017	-
dc.identifier.citation	Formalized Mathematics, Volume 25, Issue 3, Pages 185–195	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/6293	-
dc.description.abstract	SummaryIn this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	commutative algebra	-
dc.subject	polynomials	-
dc.subject	algebraic closed fields	-
dc.title	On Roots of Polynomials and Algebraically Closed Fields	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2017-0018	-
dc.description.Affiliation	Institute of Informatics, University of Gdańsk, Poland	-
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	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	Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363–371, 2016. doi:10.15439/2016F520.	-
dc.description.references	H. Heuser. Lehrbuch der Analysis. B.G. Teubner Stuttgart, 1990.	-
dc.description.references	Nathan Jacobson. Basic Algebra I. 2nd edition. Dover Publications Inc., 2009.	-
dc.description.references	Heinz Lüneburg. Gruppen, Ringe, Körper: Die grundlegenden Strukturen der Algebra. Oldenbourg Verlag, 1990.	-
dc.description.references	Knut Radbruch. Algebra I. Lecture Notes, University of Kaiserslautern, Germany, 1991.	-
dc.description.references	Christoph Schwarzweller and Agnieszka Rowińska-Schwarzweller. Schur’s theorem on the stability of networks. Formalized Mathematics, 14(4):135–142, 2006. doi:10.2478/v10037-006-0017-9.	-
dc.description.references	Christoph Schwarzweller, Artur Korniłowicz, and Agnieszka Rowińska-Schwarzweller. Some algebraic properties of polynomial rings. Formalized Mathematics, 24(3):227–237, 2016. doi:10.1515/forma-2016-0019.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	25	-
dc.description.issue	3	-
dc.description.firstpage	185	-
dc.description.lastpage	195	-
dc.identifier.citation2	Formalized Mathematics	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2017, Volume 25, Issue 3

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