MATH 327 Algebra II: Rings and Modules
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Rings, Polynomial Rings, Matrix Rings, Group Rings, Ring Homomorphism, Quotient Rings, Ideals, Ring of Fractions, the Chinese Remainder Theorem, Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains, Irreducibility Criteria, Göbner Basis, Modules, Quotient Modules, Module Homomorphisms, Generation of Modules, Direct Sums, Free Module, Tensor Product, Exact Sequences, Projective, Injective, and Flat Modules, Vector Spaces, Linear Transformation Matrices, Dual Vector Spaces, Determinants, Tensor Algebras, Symmetric and Exterior Algebras, Modules over Principal Ideal Domains, Rational Canonical Form, Jordan Canonical Form.
Credit units: 3 ECTS Credit units: 5, Prerequisite:
MATH 123 and MATH 223.
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