909 Extra Problems Commutative Algebra

Commutative Algebra

  • Show that a finitely generated module over a Noetherian local ring is flat iff it is free using Nakayama and Tor.

  • Show that 2,x  is not a principal ideal.

  • Let R be a Noetherian ring and A,B algebras over R. Suppose A is finite type over R and finite over B. Then B is finite type over R.