Matches in DBpedia 2015-10 for { ?s ?p "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."@en }
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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.".