Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homogenous Polynomials and Algebraically Independent Sets

  1. Apr 9, 2009 #1
    So I am going through Serge Lang's Algebra and he left a proof as an exercise, and I simply can't figure it out... I was wondering if someone could point me in the right direction:

    If f is a polynomial in n-variables over a commutative ring A, then f is homogeneous of degree d if and only if for every set {u, t1,t2,....tn} of (n+1) algebraically independent variables over A we have f(ut1, ut2,....utn) = u^d*f(t1,t2,...tn).

    The <= implication seems easy enough, although I don't see why we'd need algebraic independence; however, the other way has me tripped up - I just learned about algebraic independence so I'm rough around the edges. Thanks for any help!
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted