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:(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Homogenous Polynomials and Algebraically Independent Sets

Can you offer guidance or do you also need help?

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