Number of generators of a Cohen-Macaulay ideal
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چکیده
منابع مشابه
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
Let be a local Cohen-Macaulay ring with infinite residue field, an Cohen - Macaulay module and an ideal of Consider and , respectively, the Rees Algebra and associated graded ring of , and denote by the analytic spread of Burch’s inequality says that and equality holds if is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of as In this paper we ...
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Let be a commutative Noetherian ring and let I be a proper ideal of . D’Anna and Fontana in [6] introduced a new construction of ring, named amalgamated duplication of along I. In this paper by considering the ring homomorphism , it is shown that if , then , also it is proved that if , then there exists such that . Using this result it is shown that if is generically Cohen-Macaulay (resp. gen...
متن کاملAbsolute Bounds on the Number of Generators of Cohen-macaulay Ideals of Height at Most 2
For a Noetherian local domain A, there exists an upper bound Nτ (A) on the minimal number of generators of any height two ideal a for which A/a is Cohen-Macaulay of type τ . More precisely, we may take Nτ (A) := (τ + 1)eh(A), where eh(A) is the homological multiplicity of A.
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For a Noetherian local domain A, there exists an upper bound Nτ (A) on the minimal number of generators of any height two ideal a for whichA/a is Cohen-Macaulay of type τ . If A contains an infinite field, then we may take Nτ (A) := (τ + 1)ehom(A), where ehom(A) is the homological multiplicity of A.
متن کاملResults on Hilbert coefficients of a Cohen-Macaulay module
Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...
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تاریخ انتشار 2004