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- Nagata_ring abstract "In commutative algebra, an integral domain Ais called an N−1 ring if its integral closure in its quotient field is a finitely generated A module. Itis called a Japanese ring (or an N−2 ring) if for everyfinite extension L of its quotient field K, the integral closure of A in L is a finitely generated A module (or equivalently a finite A-–algebra). A ring is called universally Japanese if every finitely generated integral domain over it is Japanese, and is called a Nagata ring, named for Masayoshi Nagata, (or a pseudo–geometric ring) if it is Noetherian and universally Japanese (or, which turns out to be the same, if it is Noetherian and all of its quotients by a prime ideal are N−2 rings.) A ring is called geometric if it is the local ring of an algebraic variety or a completion of such a local ring (Danilov 2001), but this concept is not used much.".
- Nagata_ring wikiPageExternalLink 032E.
- Nagata_ring wikiPageExternalLink item?id=PMIHES_1964__20__5_0.
- Nagata_ring wikiPageID "10092186".
- Nagata_ring wikiPageLength "4023".
- Nagata_ring wikiPageOutDegree "22".
- Nagata_ring wikiPageRevisionID "648972311".
- Nagata_ring wikiPageWikiLink Category:Algebraic_geometry.
- Nagata_ring wikiPageWikiLink Category:Commutative_algebra.
- Nagata_ring wikiPageWikiLink Commutative_algebra.
- Nagata_ring wikiPageWikiLink Dedekind_domain.
- Nagata_ring wikiPageWikiLink Discrete_valuation_ring.
- Nagata_ring wikiPageWikiLink Excellent_ring.
- Nagata_ring wikiPageWikiLink Field_extension.
- Nagata_ring wikiPageWikiLink Field_of_fractions.
- Nagata_ring wikiPageWikiLink Finitely_generated_module.
- Nagata_ring wikiPageWikiLink Formal_power_series.
- Nagata_ring wikiPageWikiLink Integral_closure.
- Nagata_ring wikiPageWikiLink Integral_domain.
- Nagata_ring wikiPageWikiLink Integral_element.
- Nagata_ring wikiPageWikiLink Integrally_closed_domain.
- Nagata_ring wikiPageWikiLink Masayoshi_Nagata.
- Nagata_ring wikiPageWikiLink Noetherian.
- Nagata_ring wikiPageWikiLink Noetherian_ring.
- Nagata_ring wikiPageWikiLink Perfect_field.
- Nagata_ring wikiPageWikiLink Polynomial_ring.
- Nagata_ring wikiPageWikiLink Power_series_ring.
- Nagata_ring wikiPageWikiLink Prime_ideal.
- Nagata_ring wikiPageWikiLink Principal_ideal_domain.
- Nagata_ring wikiPageWikiLink Quasi-excellent_ring.
- Nagata_ring wikiPageWikiLink Quotient_field.
- Nagata_ring wikiPageWikiLink Quotient_ring.
- Nagata_ring wikiPageWikiLinkText "Nagata ring".
- Nagata_ring author "V.I. Danilov".
- Nagata_ring hasPhotoCollection Nagata_ring.
- Nagata_ring id "G/g044300".
- Nagata_ring title "geometric ring".
- Nagata_ring wikiPageUsesTemplate Template:Citation.
- Nagata_ring wikiPageUsesTemplate Template:Harv.
- Nagata_ring wikiPageUsesTemplate Template:Harvtxt.
- Nagata_ring wikiPageUsesTemplate Template:Springer.
- Nagata_ring subject Category:Algebraic_geometry.
- Nagata_ring subject Category:Commutative_algebra.
- Nagata_ring comment "In commutative algebra, an integral domain Ais called an N−1 ring if its integral closure in its quotient field is a finitely generated A module. Itis called a Japanese ring (or an N−2 ring) if for everyfinite extension L of its quotient field K, the integral closure of A in L is a finitely generated A module (or equivalently a finite A-–algebra).".
- Nagata_ring label "Nagata ring".
- Nagata_ring sameAs m.02q1k7j.
- Nagata_ring sameAs Q6958665.
- Nagata_ring sameAs Q6958665.
- Nagata_ring sameAs 永田環.
- Nagata_ring wasDerivedFrom Nagata_ring?oldid=648972311.
- Nagata_ring isPrimaryTopicOf Nagata_ring.