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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.

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.


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

Last Updated: May 2015


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For more information on instructors and sections for Fall 2017, please see our Fall 2017 Teaching Schedule Page

For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page


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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