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Laddar... Free Ideal Rings and Localization in General Ringsav P. M. Cohn
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Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note. Inga biblioteksbeskrivningar kunde hittas. |
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Google Books — Laddar... GenrerMelvil Decimal System (DDC)512.4Natural sciences and mathematics Mathematics Algebra Rings, integral domains, idealsKlassifikation enligt LCBetygMedelbetyg: Inga betyg.Är det här du? |