1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Free modules

  1. Dec 31, 2008 #1
    View attachment Exampleoflatex.pdf

    Let R be a commutative ring with 1. If F is a free module of rank n < 1, then show that
    HomR(F;M) is isomorphic to M^n, for each R-module M.

    I was thinking about defining a map
    Psi : HomR(F;M)--> M^n by psi(f) = (f(e1); f(e2); ... ; f(en))
    where F is free on (e1; ... ; en) and
    show Psi is an isomorphism. But I am having difficulties showing it is onto.
    Last edited: Dec 31, 2008
  2. jcsd
  3. Dec 31, 2008 #2
    Oh, I think I can use the Universal property of free modules to get the onto part.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Free modules
  1. Modules and Ideals (Replies: 1)

  2. Module and Ideal (Replies: 1)

  3. Definition of a Module (Replies: 2)