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Cohen
Cohen may refer to: Places *Cohen-kuhi Tau/4, a star 420 light-years away from Earth in the Taurus Constellation *The Cohen Building of ''The Judd School'' in Tonbridge, England People * Cohen (surname), a common Jewish surname Arts, entertainment, and media *Matt Cohen Prize, an award given annually by the Writers' Trust of Canada to a Canadian writer * Shaughnessy Cohen Award, a Canadian literary award Law * Clinger–Cohen Act, a United States federal law that is designed to improve the way the federal government acquires and manages information technology *'' Cohen v. California'', a U.S. Supreme Court case dealing with freedom of speech *'' Cohen v. Cowles Media Co.'', a U.S. Supreme Court case establishing that freedom of the press does not exempt newspapers from generally applicable laws *''Cohens v. Virginia'', a U.S. Supreme Court decision most noted for the Marshall Court's assertion of its power to review state supreme court decisions in criminal law matters *'' Flas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cohen–Macaulay Ring
In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central role in commutative algebra: they form a very broad class, and yet they are well understood in many ways. They are named for , who proved the unmixedness theorem for polynomial rings, and for , who proved the unmixedness theorem for formal power series rings. All Cohen–Macaulay rings have the unmixedness property. For Noetherian local rings, there is the following chain of inclusions. Definition For a commutative Noetherian local ring ''R'', a finite (i.e. finitely generated) ''R''-module M\neq 0 is a ''Cohen-Macaulay module'' if \mathrm(M) = \mathrm(M) (in general we have: \mathrm(M) \leq \mathrm(M), see Auslander–Buchsbaum formula for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |