Credits -- 3 (3-0-0)
Term Offered -- Spring
- Possible Text
-- - Algebra by M.
Artin.
- Topics
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-- Rings: basic definitions, homomorphisms, ideals, quotient rings,
adjunction of elements, integral domains, fraction fields, maximal
ideals and algebraic geometry
-- Factorization: integers and polynomials, unique factorization domains,
principal ideal domains, Euclidean domains, Gauss' Lemma, primes in
Z[i], algebraic integers, real and imaginary quadratic fields,
ideal factorization, ideal classes
-- Modules: matrices, free modules, bases, permanence of identities,
diagonalization of integer matrices, generators and relations,
application to abelian groups and linear operators, rational
canonical and Jordan form, polynomial rings
-- Fields: algebraic and transcendental elements, field extensions and
degree, ruler and compass constructions, finite fields, function fields
-- Galois Theory: quadratic, cubic, quartic, and quintic equations,
symmetric functions, primitive elements, Kummer and cyclotomic
extensions, the Galois group and the Galois correspondence