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


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.

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

Last Updated: May 2015

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530