Noncommutative Rings by Michael Artin

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About this book :-
Michael Artin’s Noncommutative Rings is a set of graduate-level lecture notes that explore the structure and theory of rings where multiplication is not necessarily commutative. The text warmly clarity and depth, often used in advanced algebra courses. This text is covered the Noncommutative Rings's following topics Morita equivalence (Hom, Bimodules, Projective modules etc), Localization and Goldie's theorem, Artin–Wedderburn theorem, Central simple algebras, division algebras and the Brauer group, Maximal orders, PI-rings, Irreducible representations, Growth of algebras. The beginning of the course (diamond lemma, Peirce decomposition, density and Wedderburn theory) because author began writing notes some time after the semester begain.

Book Detail :-
This book has following details information.
Title: Noncommutative Rings by Michael Artin by NA
Publisher: Michael Artin
Series: eBookDirectory
Year: 1999
Pages: 103
Type: PDF
Language: English
ISBN-10 #: N\A
ISBN-13 #: N\A
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
Part-I Morita equivalence 1. Hom 2. Bimodules 3. Projective modules 4. Tensor products 5. Functors 6. Direct limits 7. Adjoint functors 8. Morita equivalence Part-II Localization and Goldie’s theorem 1. Terminology 2. Ore sets 3. Construction of the ring of fractions 4. Modules of fractions 5. Essential submodules and Goldie rank 6. Goldie’s theorem Part-III Central simple algebras and the Brauer group 1. Tensor product algebras 2. Central simple algebras 3. Skolem-Noether theorem 4. Commutative subfields of central simple algebras 5. Faithful flatness 6. Amitsur complex 7. Interlude: analogy with bundles 8. Characteristic polynomial for central simple algebras 9. Separable splitting fields 10. Structure constants 11. Smooth maps and idempotents 12. Azumaya algebras 13. Dimension of a variety 14. Background on algebraic curves 15. Tsen’s theorem Part-IV Maximal orders 1. Lattices and orders 2. Trace pairing on Azumaya algebras 3. Separable algebras 4. Maximal orders in separable algebras 5. Hensel’s lemma 6. Maximal orders over complete discrete valuation rings 7. Recovering data from the completion 8. Addendum to Chapter III Part-V Irreducible representations 1. Definition 2. Examples 3. Standard identities 4. Central polynomials 5. Polynomial identity rings 6. Kaplansky’s theorem 7. Amitsur’s theorem 8. Posner’s theorem 9. Intrinsic characterization of Azumaya algebras 10. Irreducible representations of the free ring 11. The case of two 2 × 2 matrices X, Y 12. Some tensor notation 13. The main theorem of invariant theory 14. Procesi’s theorem 15. The spectrum of the ring of generic matrices Part-VI Growth of algebras 1. Growth functions 2. Warfield’s theorem 3. Path algebras 4. Bergman’s gap theorem 5. Theorem of Stephenson and Zhang 6. Projective covers 7. Hilbert functions of graded algebras of finite global dimension 8. Modules with linear growth 9. Theorem of Small and Warfield

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