Yoshiro Mori (mathematician)
Yoshiro Mori is a Japanese mathematician working on commutative algebra who introduced the Mori–Nagata theorem and whose work led to Mori domain In algebra, a Mori domain, named after Yoshiro Mori by , is an integral domain satisfying the ascending chain condition on integral divisorial ideals. Noetherian domains and Krull domain In commutative algebra, a Krull ring, or Krull domain, is ...s. References * 20th-century Japanese mathematicians Year of birth missing Possibly living people Place of birth missing {{Japan-mathematician-stub ...
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Mori–Nagata Theorem
In algebra, the Mori–Nagata theorem introduced by and , states the following: let ''A'' be a noetherian reduced commutative ring with the total ring of fractions ''K''. Then the integral closure of ''A'' in ''K'' is a direct product of ''r'' Krull domains, where ''r'' is the number of minimal prime ideals of ''A''. The theorem is a partial generalization of the Krull–Akizuki theorem, which concerns a one-dimensional noetherian domain. A consequence of the theorem is that if ''R'' is a Nagata ring In commutative algebra, an N-1 ring is an integral domain A whose integral closure in its quotient field is a finitely generated A- module. It is called a Japanese ring (or an N-2 ring) if for every finite extension L of its quotient field K, the i ..., then every ''R''-subalgebra of finite type is again a Nagata ring . The Mori–Nagata theorem follows from Matijevic's theorem. References * * * * Commutative algebra Theorems in ring theory {{abstract-algebra-stub ...