Modules Satisfying the S-Noetherian Property and S-ACCR |
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Authors: | Hamed Ahmed Hizem Sana |
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Affiliation: | 1. Department of Mathematics, Faculty of Sciences, Monastir, Tunisiahamed.ahmed@hotmail.fr;3. Department of Mathematics, Faculty of Sciences, Monastir, Tunisia |
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Abstract: | Let A = k[x1,..., xn] be a standard graded k-algebra over an infinite field k. We assume A is Cohen-Macaulay and has Krull dimension one. Let e denote the multiplicity of A and r - 1 the postulation number of A. Let I be a homogeneous ideal in A of grade one. Let j(I) denote the smallest degree of a regular form in I. Let l (I) denote the smallest power of (x1,... , xn) contained in I. If μ(I) denotes the minimum number of generators of I, then we show μ(I) ≤ e + j(I) - max{r,l(I)}, We then show how Dubreil's Second Theorem follows easily from this inequality |
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Keywords: | S-Noetherian S-ACCR |
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