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Introduction to noncommutative algebra / Matej Bresar.

By: Material type: TextTextSeries: UniversitextPublication details: Switzerland : Springer, 2014.Description: xxxvii, 199 pISBN:
  • 9783319086927
Subject(s): DDC classification:
  • 512.46 23 B842
Contents:
1. Finite Dimensional Division Algebras -- 2. Structure of Finite Dimensional Algebras -- 3. Modules and Vector Spaces -- 4. Tensor Products -- 5. Structure of Rings -- 6. Noncommutative Polynomials -- 7. Rings of Quotients and Structure of PI-Rings-- References-- Index.
Summary: This book begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 512.46 B842 (Browse shelf(Opens below)) Available 135834
Total holds: 0

Includes bibliographical references and index.

1. Finite Dimensional Division Algebras --
2. Structure of Finite Dimensional Algebras --
3. Modules and Vector Spaces --
4. Tensor Products --
5. Structure of Rings --
6. Noncommutative Polynomials --
7. Rings of Quotients and Structure of PI-Rings--
References--
Index.

This book begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

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