J=sum from i=1->n of <X_i^q - X_i>(adsbygoogle = window.adsbygoogle || []).push({});

V={polynomials f with deg in X_i < q)

k is a field with q elements. k[X] is the polynomial ring in "n" variables".

i am supposed to prove that V+J=k[x].

i was told that this could be done with induction for the number "k", by using the following notion.given a polynomial f E k[x]:

k0=the sum of L_j. j=1..."number of monomials".

L_j is the sum of of the "degrees" of the "indeterminates/variables" which are >q in monomial "j".

so L_j=sum of all s_i, where s_i > q. s_i are the exponents of the monomial which are >q.

so somehow i have to show that this is true for <k0 and then it is true for k0. or something like that?

does anyone know what i'm saying here? it might be a little confusing. just ask if there's anything you don't understand.

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# Proving that V+J=k[x]

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