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[ subject:"Associative algebras." ]
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Free ideal rings and localization in...
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Cohn, P. M.
Free ideal rings and localization in general rings /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
杜威分類號:
512.4
書名/作者:
Free ideal rings and localization in general rings // P.M. Cohn.
其他題名:
Free Ideal Rings & Localization in General Rings
作者:
Cohn, P. M.
面頁冊數:
1 online resource (xxii, 572 pages) : : digital, PDF file(s).
附註:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:
Rings (Algebra)
標題:
Ideals (Algebra)
標題:
Associative algebras.
ISBN:
9780511542794 (ebook)
摘要、提要註:
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.
電子資源:
http://dx.doi.org/10.1017/CBO9780511542794
Free ideal rings and localization in general rings /
Cohn, P. M.
Free ideal rings and localization in general rings /
Free Ideal Rings & Localization in General RingsP.M. Cohn. - 1 online resource (xxii, 572 pages) :digital, PDF file(s). - New mathematical monographs ;3. - New mathematical monographs ;3..
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Generalities on rings and modules --1.
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.
ISBN: 9780511542794 (ebook)Subjects--Topical Terms:
486779
Rings (Algebra)
LC Class. No.: QA247 / .C636 2006
Dewey Class. No.: 512.4
Free ideal rings and localization in general rings /
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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.
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http://dx.doi.org/10.1017/CBO9780511542794
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