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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
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