TY - BOOK ID - 78344 TI - Introduction to Algebraic K-Theory. (AM-72), Volume 72 PY - 2016 VL - 72 SN - 0691081018 9780691081014 140088179X 9781400881796 PB - Princeton, NJ DB - UniCat KW - Algebraic geometry KW - Ordered algebraic structures KW - Associative rings KW - Abelian groups KW - Functor theory KW - Anneaux associatifs KW - Groupes abéliens KW - Foncteurs, Théorie des KW - 512.73 KW - 515.14 KW - Functorial representation KW - Algebra, Homological KW - Categories (Mathematics) KW - Functional analysis KW - Transformations (Mathematics) KW - Commutative groups KW - Group theory KW - Rings (Algebra) KW - Cohomology theory of algebraic varieties and schemes KW - Algebraic topology KW - Abelian groups. KW - Associative rings. KW - Functor theory. KW - 515.14 Algebraic topology KW - 512.73 Cohomology theory of algebraic varieties and schemes KW - Groupes abéliens KW - Foncteurs, Théorie des KW - Abelian group. KW - Absolute value. KW - Addition. KW - Algebraic K-theory. KW - Algebraic equation. KW - Algebraic integer. KW - Banach algebra. KW - Basis (linear algebra). KW - Big O notation. KW - Circle group. KW - Coefficient. KW - Commutative property. KW - Commutative ring. KW - Commutator. KW - Complex number. KW - Computation. KW - Congruence subgroup. KW - Coprime integers. KW - Cyclic group. KW - Dedekind domain. KW - Direct limit. KW - Direct proof. KW - Direct sum. KW - Discrete valuation. KW - Division algebra. KW - Division ring. KW - Elementary matrix. KW - Elliptic function. KW - Exact sequence. KW - Existential quantification. KW - Exterior algebra. KW - Factorization. KW - Finite group. KW - Free abelian group. KW - Function (mathematics). KW - Fundamental group. KW - Galois extension. KW - Galois group. KW - General linear group. KW - Group extension. KW - Hausdorff space. KW - Homological algebra. KW - Homomorphism. KW - Homotopy. KW - Ideal (ring theory). KW - Ideal class group. KW - Identity element. KW - Identity matrix. KW - Integral domain. KW - Invertible matrix. KW - Isomorphism class. KW - K-theory. KW - Kummer theory. KW - Lattice (group). KW - Left inverse. KW - Local field. KW - Local ring. KW - Mathematics. KW - Matsumoto's theorem. KW - Maximal ideal. KW - Meromorphic function. KW - Monomial. KW - Natural number. KW - Noetherian. KW - Normal subgroup. KW - Number theory. KW - Open set. KW - Picard group. KW - Polynomial. KW - Prime element. KW - Prime ideal. KW - Projective module. KW - Quadratic form. KW - Quaternion. KW - Quotient ring. KW - Rational number. KW - Real number. KW - Right inverse. KW - Ring of integers. KW - Root of unity. KW - Schur multiplier. KW - Scientific notation. KW - Simple algebra. KW - Special case. KW - Special linear group. KW - Subgroup. KW - Summation. KW - Surjective function. KW - Tensor product. KW - Theorem. KW - Topological K-theory. KW - Topological group. KW - Topological space. KW - Topology. KW - Torsion group. KW - Variable (mathematics). KW - Vector space. KW - Wedderburn's theorem. KW - Weierstrass function. KW - Whitehead torsion. KW - K-théorie UR - https://www.unicat.be/uniCat?func=search&query=sysid:78344 AB - 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. ER -