ADVANCED ALGEBRA I

Credit Hours: 3 · Graduate

This course will cover graduate level topics in group theory, ring theory, and module theory. Specific topics include the isomorphism theorems for groups, rings, and modules; group actions; solvable and nilpotent groups; Sylow’s theorems; semi-direct products of groups; ideals; rings of fractions; various unique factorization domains; Hilbert’s Basis Theorem; Gröbner Bases; tensor product of modules and universal property; modules over principal ideal domains; and canonical forms. The course will also include an introduction to category theory as time permits. Graduate/Undergraduate Equivalency: MATH 463 . Mutually Exclusive: Cannot register for MATH 563 if student has credit for MATH 463 .