## Illinois Journal of Mathematics

### Monomial sequences of linear type

Hamid Kulosman

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 18 November 2009

https://projecteuclid.org/euclid.ijm/1258554358

Digital Object Identifier
doi:10.1215/ijm/1258554358

Mathematical Reviews number (MathSciNet)
MR2595763

Zentralblatt MATH identifier
1182.13005

#### Citation

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

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