MATH 228 - Algebra: Introduction to Ring Theory

★ 3 (fi 6) (either term, 3-0-0) Integers. Mathematical induction. Equivalence relations. Commutative rings, including the integers mod n, complex numbers and polynomials. The Chinese remainder theorem. Fields and integral domains. Euclidean domains, principal ideal domains and unique factorization. Quotient rings and homomorphisms. Construction of finite fields. Applications such as public domain encryption, Latin squares and designs, polynomial error detecting codes, and/or addition and multiplication of large integers. Prerequisite: Any linear algebra course. Credit for MATH 228 cannot be obtained if credit for MATH 326 has been already obtained.