Mathematics Department - Math 552 - Abstract Algebra II

Math 552 - Abstract Algebra II

This is a standard course for second semester graduate students. It covers fields and Galois Theory, basic Ring & Module theory, and elementary homological algebra.

Prerequisites: Algebra I (640:551) or its equivalent

Basic Field Theory: Galois groups, separable and inseparable extensions, solutions of equations, finite fields.
Noetherian rings: chain conditions, Hilbert Basis Theorem, Noether normalization, Hilbert Nullstellensatz.
Basic module theory: Tensor Product, Projective and injective modules, resolutions, baby homological algebra.
Finite-dimensional algebras: Simple and semisimple algebras, Artin-Wedderburn Theorem, group rings.

Current semester (Spring 2017)

Prof. Tunnell
Main Text: N. Jacobson, Basic Algebra I, II

Previous Semesters

Last updated: May 21, 2015

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