Description

Ring theory is a subject of central importance in
algebra, has deep connections with various branches
of mathematics---including analysis and topology, and
has become increasingly important to computer science
and physics.

This course is intended for graduate students
in mathematics, both pure and applied.

Objectives

While preparing for the comprehensive exam in algebra,
this course gives a general introduction to the theory
of associative rings. The topics covered include
Wedderburn-Artin theory, Jacobson radical theory, prime
and primitive rings, perfect and semiperfect rings, as
well as injective, projective and flat modules.

Prerequisites

Undergraduate courses of Abstract Algebra
(such as MATH 3320).

Texts

• Israel N. Herstein, Noncommutative rings. The Carus Mathematical
  Monographs, No. 15, John Wiley & Sons, Inc., New York 1968.
• Tsit-Yuen Lam, A first course in noncommutative rings. Second edition.
  Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 2001.
• Tsit-Yuen Lam, Lectures on modules and rings. Graduate Texts in
  Mathematics, 189. Springer-Verlag, New York, 1999.