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Algebra II: Rings and Fields MATH 340 (3)
The integers, fundamental theorem of arithmetic. Equivalence relations, modular arithmetic. Univariate polynomials, unique factorization. Rings and fields. Units, zero divisors, integral domains. Ideals, ring homomorphisms. Quotient rings, the ring isomorphism theorem. Chinese remainder theorem. Euclidean, principal ideal, and unique factorization domains. Field extensions, minimal polynomials. Classification of finite fields. Prerequisite: MATH 240 with a minimum grade of C- or MATH 232 with a grade of at least B. Students with credit for MATH 332 may not take this course for further credit. Quantitative.