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An Algebraic Introduction to K-Theory

2002-05-20 Mathematics
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Release : 2002-05-20
Genre : Mathematics
Kind : eBook
Book Rating : 446/5 ( reviews)

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Book Synopsis An Algebraic Introduction to K-Theory by : Bruce A. Magurn

Download or read book An Algebraic Introduction to K-Theory written by Bruce A. Magurn. This book was released on 2002-05-20. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.

The $K$-book

2013-06-13 Mathematics
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Release : 2013-06-13
Genre : Mathematics
Kind : eBook
Book Rating : 324/5 ( reviews)

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Book Synopsis The $K$-book by : Charles A. Weibel

Download or read book The $K$-book written by Charles A. Weibel. This book was released on 2013-06-13. Available in PDF, EPUB and Kindle. Book excerpt: Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr

Introduction to Algebraic K-theory

1971 Mathematics
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Release : 1971
Genre : Mathematics
Kind : eBook
Book Rating : 014/5 ( reviews)

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Book Synopsis Introduction to Algebraic K-theory by : John Willard Milnor

Download or read book Introduction to Algebraic K-theory written by John Willard Milnor. This book was released on 1971. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

An Introduction to K-Theory for C*-Algebras

2000-07-20 Mathematics
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Release : 2000-07-20
Genre : Mathematics
Kind : eBook
Book Rating : 448/5 ( reviews)

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Book Synopsis An Introduction to K-Theory for C*-Algebras by : M. Rørdam

Download or read book An Introduction to K-Theory for C*-Algebras written by M. Rørdam. This book was released on 2000-07-20. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

Algebraic K-Theory and Its Applications

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 149/5 ( reviews)

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Book Synopsis Algebraic K-Theory and Its Applications by : Jonathan Rosenberg

Download or read book Algebraic K-Theory and Its Applications written by Jonathan Rosenberg. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.

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