On the Number of Elements Independent with Respect to an Ideal
نویسنده
چکیده
Let R denote a commutative noetherian ring, and o an ideal of R. Elements x j , . . . , x n e R are called independent with respect to a, or simply a-independent, if every form Fe R[Xlf..., X^\ such that F(xl 5. . . , xn) = 0 has all its coefficients in a. Valla [10] introduced the notation sup a for the maximal number of a-independent elements in a. He found that sup a is bounded above by the height of o (which we denote by ht a) whereas the lower bound grade a was established by Rees:
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Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module
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