A Variety of Graph Coloring Problems
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چکیده
Let k be a field and let A = C[x1, . . . , xn]. For the set of common zeros of elements of an ideal I ⊆ A, we write V(I). For the ideal of polynomials which vanish on a set V ⊆ k, we write I(V ). Given an ideal I ⊆ A, the ideal membership problem is the problem of determining whether or not a given f ∈ A is an element of the ideal I. This is difficult because the division algorithm can badly fail in this ring. The next example demonstrates that we cannot determine if f is in I by simply dividing by the generators of this ideal.
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تاریخ انتشار 2014