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Spring 2022 Algorithms for checking zero-dimensional complete intersections
Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano
J. Commut. Algebra 14(1): 61-76 (Spring 2022). DOI: 10.1216/jca.2022.14.61

Abstract

Given a 0-dimensional affine K-algebra R=K[x1,,xn]I, where I is an ideal in a polynomial ring K[x1,,xn] over a field K, or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether R is a complete intersection at a maximal ideal, whether R is locally a complete intersection, and whether R is a strict complete intersection. These algorithms are based on Wiebe’s characterization of 0-dimensional local complete intersections via the 0-th Fitting ideal of the maximal ideal. They allow us to detect which generators of I form a regular sequence resp. a strict regular sequence, and they work over an arbitrary base field K. Using degree filtered border bases, we can detect strict complete intersections in certain families of 0-dimensional ideals.

Citation

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Martin Kreuzer. Le Ngoc Long. Lorenzo Robbiano. "Algorithms for checking zero-dimensional complete intersections." J. Commut. Algebra 14 (1) 61 - 76, Spring 2022. https://doi.org/10.1216/jca.2022.14.61

Information

Received: 22 March 2019; Revised: 5 August 2019; Accepted: 5 August 2019; Published: Spring 2022
First available in Project Euclid: 31 May 2022

Digital Object Identifier: 10.1216/jca.2022.14.61

Subjects:
Primary: 13C40
Secondary: 13H10 , 13P99 , 14M10 , 14Q99

Keywords: border basis , complete intersection , Fitting ideal , locally complete intersection , strict complete intersection , zero-dimensional affine algebra , zero-dimensional scheme

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.14 • No. 1 • Spring 2022
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