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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 a ...s. References * 20th-century Japanese mathematicians Year of birth missing Possibly living people Place of birth missing {{Japan-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ..., 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 a commutative ring with a well behaved theory of prime factorization. They were introduced by Wolfgang Krull in 1931. They are a higher-dimensional generalization of Dedekind domains, which a ...s both have this property. A commutative ring is a Krull domain if and only if it is a Mori domain and completely integrally closed.Bourbaki AC ch. VII §1 no. 3 th. 2 A polynomial ring over a Mori domain need not be a Mori domain. Also, the complete integral closure of a Mori domain need not be a Mori (or, equivalently, Krull) domain. Notes References * * * * * * *{{Citation , last1=Querré , first1=J. , title=Cours d'algèbre , url=https://books.google.com/books/about/Cours_d_alg%C3%A8bre.html?id=X1LQAAAAMAAJ , publisher=Masson , loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calendar year (the mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Possibly Living People
Possibility is the condition or fact of being possible. Latin origins of the word hint at ability. Possibility may refer to: * Probability, the measure of the likelihood that an event will occur * Epistemic possibility, a topic in philosophy and modal logic * Possibility theory, a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory * Subjunctive possibility, (also called alethic possibility) is a form of modality studied in modal logic. ** Logical possibility, a proposition that will depend on the system of logic being considered, rather than on the violation of any single rule * Possible world, a complete and consistent way the world is or could have been Other *Possible (Italy), a political party in Italy *Possible Peru, a political party in Peru *Possible Peru Alliance, an electoral alliance in Peru Entertainment *'' Kim Possible'', a US children's TV series :*Kim Possible (character), the central character of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
