Dummit And Foote Solutions Chapter 10.zip

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Here is the detailedsyllabus of the course:January:K-Theory*Introduction to the theory of rings and groups andK0(X). *Ring and module theory including ring and group homomorphisms, ideals,the structure of Z/pZ (Dummit & Foote, chapter 2), and thetheory of finite abelian groups (Dummit & Foote, chapter 3).*The theory of modules over a PID, including* Homomorphism of modules (not necessarily linear),* Projective modules,* Modules over a PID: Wedderburn decomposition and Ore extensions,* The Galois correspondence (separable field extensions, separable groupextensions, field extensions, separable homomorphisms, separable group homomorphisms),* Field extensions, separable extensions, algebraic closures of fields,fundamental theorem of Galois theory, separable field extensions, separable group extensions, separable homomorphisms, separable group homomorphisms, linear and inseparable extensions, separable field extensions, inseparable extensions, field extensions, separable extensions, separable group extensions, separable homomorphisms, separable group homomorphisms. * The fundamental theorem of Galois theory. * The inverse Galois problem. * Algebraic and transcendental extensions; separable and inseparableextensions. (Dummit & Foote, Chapter 4 and Sections 5.2-5.4)* Splitting fields and algebraic closure of fields. Galois groups. Thefundamental theorem of Galois theory. Applications to solving equationsby radicals. Finite and cyclotomic fields. * Theory of finite fields.* Finite abelian groups. * Algebraic number theory. Algebraic extensions of the rational numbers, Riemann zeta function. Fundamental theorems of algebraic number theory. Polynomials with integer coefficients. Rational and algebraic integers. Real numbers and their extensions. * Applications to solving equations by radicals. * Field automorphisms, isomorphisms, unitary groups, the fundamentaltheorem of Galois theory. * Geometric progressions and geometric sequences. 827ec27edc