MATH 403 A: Introduction to Modern Algebra

Elementary theory of rings and fields: polynomial rings. Ideals, homomorphisms, quotients, and fundamental isomorophism theorems. Fields and maximal ideals. Euclidean rings. Field extensions. Algebraic extensions. Vector spaces and degrees of extensions. Adjoining roots of polynomials. Finite fields. Straight edge and compass constructions. Prerequisite: minimum grade of 2.0 in MATH 402. Offered: W.