Zariski Topology

Pole DC	Wartość	Język
dc.contributor.author	Watase, Yasushige	-
dc.date.accessioned	2019-03-06T12:24:00Z	-
dc.date.available	2019-03-06T12:24:00Z	-
dc.date.issued	2018	-
dc.identifier.citation	Formalized Mathematics, Volume 26, Issue 4, Pages 277-283	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7639	-
dc.description.abstract	We formalize in the Mizar system [3], [4] basic definitions of commutative ring theory such as prime spectrum, nilradical, Jacobson radical, local ring, and semi-local ring [5], [6], then formalize proofs of some related theorems along with the first chapter of [1].The article introduces the so-called Zariski topology. The set of all prime ideals of a commutative ring A is called the prime spectrum of A denoted by Spectrum A. A new functor Spec generates Zariski topology to make Spectrum A a topological space. A different role is given to Spec as a map from a ring morphism of commutative rings to that of topological spaces by the following manner: for a ring homomorphism h : A → B, we defined (Spec h) : Spec B → Spec A by (Spec h)(𝔭) = h−1(𝔭) where 𝔭 2 Spec B.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	prime spectrum	-
dc.subject	local ring	-
dc.subject	semi-local ring	-
dc.subject	nilradical	-
dc.subject	Jacobson radical	-
dc.subject	Zariski topology	-
dc.title	Zariski Topology	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2018-0024	-
dc.description.Affiliation	Suginami-ku Matsunoki, 3-21-6 Tokyo, Japan	-
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dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	-
dc.description.references	Shigeru Iitaka. Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties. Springer-Verlag New York, Inc., 1982.	-
dc.description.references	Shigeru Iitaka. Ring Theory (in Japanese). Kyoritsu Shuppan Co., Ltd., 2013.	-
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dc.identifier.eissn	1898-9934	-
dc.description.volume	26	-
dc.description.issue	4	-
dc.description.firstpage	277	-
dc.description.lastpage	283	-
dc.identifier.citation2	Formalized Mathematics	-
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