A shape lemma for ideals of differential operators

Manuel Kauers; Christoph Koutschan; Thibaut Verron

doi:10.1016/j.jalgebra.2025.04.015

A shape lemma for ideals of differential operators

Manuel Kauers^*
, Christoph Koutschan
, Thibaut Verron

^*Corresponding author for this work

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

We propose a version of the classical shape lemma for zero-dimensional ideals of a commutative multivariate polynomial ring to the noncommutative setting of zero-dimensional ideals in an algebra of differential operators.

Original language	English
Pages (from-to)	448-459
Number of pages	12
Journal	Journal of Algebra
Volume	677
DOIs	https://doi.org/10.1016/j.jalgebra.2025.04.015
Publication status	Published - Sept 2025

Fields of science

101013 Mathematical logic
101 Mathematics
102031 Theoretical computer science
101005 Computer algebra
101001 Algebra

JKU Focus areas

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10.1016/j.jalgebra.2025.04.015Licence: CC BY

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title = "A shape lemma for ideals of differential operators",

abstract = "We propose a version of the classical shape lemma for zero-dimensional ideals of a commutative multivariate polynomial ring to the noncommutative setting of zero-dimensional ideals in an algebra of differential operators.",

author = "Manuel Kauers and Christoph Koutschan and Thibaut Verron",

year = "2025",

month = sep,

doi = "10.1016/j.jalgebra.2025.04.015",

language = "English",

volume = "677",

pages = "448--459",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Elsevier",

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TY - JOUR

T1 - A shape lemma for ideals of differential operators

AU - Kauers, Manuel

AU - Koutschan, Christoph

AU - Verron, Thibaut

PY - 2025/9

Y1 - 2025/9

N2 - We propose a version of the classical shape lemma for zero-dimensional ideals of a commutative multivariate polynomial ring to the noncommutative setting of zero-dimensional ideals in an algebra of differential operators.

AB - We propose a version of the classical shape lemma for zero-dimensional ideals of a commutative multivariate polynomial ring to the noncommutative setting of zero-dimensional ideals in an algebra of differential operators.

UR - https://www.scopus.com/pages/publications/105003702235

U2 - 10.1016/j.jalgebra.2025.04.015

DO - 10.1016/j.jalgebra.2025.04.015

M3 - Article

SN - 0021-8693

VL - 677

SP - 448

EP - 459

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A shape lemma for ideals of differential operators

Abstract

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