Algebra

Abelian Groups and Classification of Finite Abelian Groups Modules over PIDs Smith Normal Form and Invariant Factors Cyclic Module Decompositions Tensor Products of Modules Hom Functors and Module Homomorphisms Ext Functors and Module Extensions Tor Functors and Projective Resolutions Projective Modules Exact Sequences of Modules Polynomial Rings and Ring Homomorphism Kernels Ideals and Quotient Rings Prime and Maximal Ideals Radical Ideals and Nilradicals Noether Normalization Integral Closure Chinese Remainder Theorem and Product Decompositions Affine Algebraic Geometry and Residue Fields Ideals in Quadratic Integer Rings and Exterior Powers Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization