## Osaka Journal of Mathematics

### On linear resolution of powers of an ideal

Keivan Borna

#### Abstract

In this paper we give a generalization of a result of Herzog, Hibi, and Zheng providing an upper bound for regularity of powers of an ideal. As the main result of the paper, we give a simple criterion in terms of Rees algebra of a given ideal to show that high enough powers of this ideal have linear resolution. We apply the criterion to two important ideals $J,J_{1}$ for which we show that $J^{k}$, and $J_{1}^{k}$ have linear resolution if and only if $k\neq 2$. The procedures we include in this work is encoded in computer algebra package CoCoA [3].

#### Article information

Source
Osaka J. Math., Volume 46, Number 4 (2009), 1047-1058.

Dates
First available in Project Euclid: 15 December 2009

https://projecteuclid.org/euclid.ojm/1260892839

Mathematical Reviews number (MathSciNet)
MR2604920

Zentralblatt MATH identifier
1183.13016

#### Citation

Borna, Keivan. On linear resolution of powers of an ideal. Osaka J. Math. 46 (2009), no. 4, 1047--1058. https://projecteuclid.org/euclid.ojm/1260892839

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