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  3. Free Ideal Rings and Localization in General Rings
  • Cited by 110
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    • Publisher:
      Cambridge University Press
      Publication date:
      22 August 2009
      08 June 2006
      ISBN:
      9780511542794
      9780521853378
      DOI:
      https://doi.org/10.1017/CBO9780511542794
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.961kg, 594 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      New Mathematical Monographs (3)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    New Mathematical Monographs (3)
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    Book description

    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.

    Reviews

    'This book presents the theory of free ideal rings (firs) in detail.'

    Source: L'enseignement mathematique

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