Commutative Algebra/Print version

Objects and morphisms Functors, natural transformations, universal arrows Kernels, cokernels, products, coproducts Diagram chasing within Abelian categories Modules, submodules and homomorphisms Generators and chain conditions The Cayley–Hamilton theorem and Nakayama's lemma Direct products, direct sums and the tensor product Fractions, annihilator Sequences of modules Torsion-free, flat, projective and free modules Basic ideal theory Nilradical and Jacobson radical Jacobson rings The spectrum and the Zariski topology Noetherian rings Primary decomposition Artinian rings Krull dimension Valuation rings Algebras and integral elements Irreducibility, algebraic sets and varieties Noether's normalisation lemma Hilbert's Nullstellensatz