denotes the real numbers. Characterize the elements that are isomorphisms.
- Prove that if A is an R-algebra, then A is an R-module.
- a) Let F be any field. Find all F-submodules of F and find all quotient modules of F.
b) Do the same as in part a), replacing the field "F" with the integers Z.
- Let M, N, K be -modules. If and then Use this to show that is a ring with identity.
- Let be a commutative ring
show that as left modules.
- Let be commutative with 1. Show that as rings. (G) See if you can find a counterexample to #10, pg. 331.
- (G) Find where