Illinois Journal of Mathematics

Monomial sequences of linear type

Hamid Kulosman

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Let $R$ be a Noetherian commutative ring, $\langle a_1,\dots, a_n\rangle$ a sequence of elements of $R$, $I=(a_1,\dots,a_n)$ the ideal generated by the elements $a_i$ and $I_i=(a_1,\dots,a_i)$, $i=0,1,\dots, n$, the ideal generated by the first $i$ elements of the sequence. A c-sequence is a sequence $\langle a_1,\dots, a_n\rangle$ which satisfies the condition \[ [I_{i-1}I^k : a_i] \cap I^k=I_{i-1}I^{k-1} \] for every $i \in\{1, \dots, n\}$ and every $k\geq1$. It generates an ideal of linear type. We characterize c-sequences in terms of the corresponding sequences in the Rees algebra of the ideal generated by the elements of the sequence. We then characterize monomial c-sequences of three terms.

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Illinois J. Math., Volume 52, Number 4 (2008), 1213-1221.

First available in Project Euclid: 18 November 2009

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Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics 13B25: Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] 13A15: Ideals; multiplicative ideal theory 13C13: Other special types


Kulosman, Hamid. Monomial sequences of linear type. Illinois J. Math. 52 (2008), no. 4, 1213--1221. doi:10.1215/ijm/1258554358.

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