Algebra

These are notes on Algebra. Much of this will, at least in the beginning, be taken up by commutative algebra lemmas to support theorems in Algebraic Geometry. That being said, as I learn more algebra, I hope to improve these notes to include more non-commutative algebra.

• 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.
• Group Theory

  These are my notes on group theory.
• Notes - Nonommutative Algebra

  These are my notes on noncommutative algebra (if I ever learn any).