18.702 Algebra II, Spring 2003

Artin, Michael

Author(s)

Artin, Michael

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Alternative title

Algebra II

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Abstract

More extensive and theoretical than the 18.700-18.703 sequence. Experience with proofs helpful. First term: group theory, geometry, and linear algebra. Second term: group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, Galois theory. From the course home page: Course Description The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.

Date issued

2003-06

URI

http://hdl.handle.net/1721.1/45579

Department

Massachusetts Institute of Technology. Department of Mathematics

Other identifiers

18.702-Spring2003

local: 18.702

local: IMSCP-MD5-10111c7712e1ce4a5fd5521721bd110a

Keywords

Sylow theorems, Group Representations, definitions, unitary representations, characters, Schur's Lemma, Rings: Basic Definitions, homomorphisms, fractions, Factorization, unique factorization, Gauss' Lemma, explicit factorization, maximal ideals, Quadratic Imaginary Integers, Gauss Primes, quadratic integers, ideal factorization, ideal classes, Linear Algebra over a Ring, free modules, integer matrices, generators and relations, structure of abelian groups, Rings: Abstract Constructions, relations in a ring, adjoining elements, Fields: Field Extensions, algebraic elements, degree of field extension, ruler and compass, symbolic adjunction, finite fields, Fields: Galois Theory, the main theorem, cubic equations, symmetric functions, primitive elements, quartic equations, quintic equations

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