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The notion of weakly relatively prime and W-Gröbner basis in K[x1, x2, …, xn] are given. The following results are obtained: for polynomials f1, f2, …, fm, is a Gröbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition...
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