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Introduction to Algebraic K-Theory
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John Milnor
Language:
English
Published/Copyright:
1972
About this book
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.
Reviews
"John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society"
"John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters"
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 2, 2016
eBook ISBN:
9781400881796
Pages and Images/Illustrations in book
Main content:
200
eBook ISBN:
9781400881796
Keywords for this book
Homomorphism; Root of unity; Elementary matrix; Subgroup; Dedekind domain; K-theory; Topological group; Complex number; Ideal (ring theory); Exterior algebra; Algebraic K-theory; Banach algebra; Vector space; Wedderburn's theorem; Ring of integers; Algebraic integer; Rational number; Division algebra; Basis (linear algebra); Cyclic group; Local field; Commutative property; Commutative ring; Direct sum; Monomial; Function (mathematics); Theorem; Quotient ring; Real number; Topological K-theory; Existential quantification; Special linear group; Variable (mathematics); Number theory; Isomorphism class; Matsumoto's theorem; Integral domain; Galois extension; Maximal ideal; Algebraic equation; General linear group; Surjective function; Homological algebra; Identity matrix; Congruence subgroup; Topological space; Coprime integers; Noetherian; Polynomial; Fundamental group; Prime ideal; Tensor product; Projective module; Division ring; Invertible matrix; Exact sequence; Kummer theory; Simple algebra; Commutator; Identity element; Abelian group; Absolute value; Topology; Special case; Hausdorff space; Prime element; Free abelian group; Direct limit; Scientific notation; Mathematics
Audience(s) for this book
College/higher education;Professional and scholarly;
