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181005 ||| eng |
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|a 9780511542794
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| 050 |
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4 |
|a QA247
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| 100 |
1 |
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|a Cohn, P. M.
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| 245 |
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|a Free ideal rings and localization in general rings
|c P.M. Cohn
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| 246 |
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1 |
|a Free Ideal Rings & Localization in General Rings
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| 260 |
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|a Cambridge
|b Cambridge University Press
|c 2006
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| 300 |
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|a xxii, 572 pages
|b digital
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| 653 |
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|a Rings (Algebra)
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| 653 |
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|a Ideals (Algebra)
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| 653 |
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|a Associative algebras
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 490 |
0 |
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|a New mathematical monographs
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| 856 |
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0 |
|u https://doi.org/10.1017/CBO9780511542794
|x Verlag
|3 Volltext
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| 082 |
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|a 512.4
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| 520 |
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|a 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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