Rings, fields, polynomials, algebras. Homomorphisms, ideals, quotients. Ring extensions, field extensions, construction of finite fields. Integral domains: Euclidean, principal ideal, unique factorization. Chain conditions. Introduction to modules. Modules over a principal ideal domain, finitely generated abelian groups, matrix canonical forms. Prerequisite MATH 227, or both MATH 225 and 228.
Rings, fields, polynomials, algebras. Homomorphisms, ideals, quotients. Ring extensions, field extensions, construction of finite fields. Integral domains: Euclidean, principal ideal, unique factorization. Chain conditions. Introduction to modules. Modules over a principal ideal domain, finitely generated abelian groups, matrix canonical forms. Prerequisite MATH 227, or both MATH 225 and 228.
