Abstract
We study ideals of the form where P i, j are ideals generated by variables {x 1, x 2,…,, x n } \\ {x i , x j } in a polynomial ring over a field. We concentrate the case that each power w i, j takes a value α or β, where α > β > 0. Our purpose is determining whether S/I is Cohen–Macaulay or not for such an ideal. We take a graph consisting of {i, j} where w i, j = α. The Cohen–Macaulayness is characterized by G.
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