Commutative Algebra

These are my notes on commutative algebra, in part to support Algebraic Geometry, and in part because I think the subject is neat.

• Properties of the Tensor Product

  Here are various results about the tensor product, one of my favorite mathematical constructions.
• Basic Commutative Ring Theory

  Here we provide some crucial defininitions and lemmas for the theory of commutative rings. All rings are commutative with unity; all homomorphisms of rings take 1 to 1.
• Graded Rings

  Here we define the projectivization of a graded ring and the projectivization of a sheaf of graded rings, and prove some important lemmas about them. We also record some important facts about graded rings. This basically follows the discussion in Hartshorne’s Algebraic Geometry, Chapter II, Section 2.