Yet another differential shape lemma

Joris van der Hoeven; Gleb Pogudin

doi:10.1016/j.jalgebra.2026.01.014

Yet another differential shape lemma

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

Abstract

Recently, Kauers, Koutschan, and Verron proved a non-commutative version of the classical shape lemma in the theory of Gröbner bases. Their result requires the ideal to be D-radical. In this note, we prove a new non-commutative shape lemma that does not require this assumption.

Original language	English
Pages (from-to)	683-689
Number of pages	7
Journal	Journal of Algebra
Volume	693
DOIs	https://doi.org/10.1016/j.jalgebra.2026.01.014
Publication status	Published - 1 May 2026

Keywords

Differential operators
Gröbner basis
Shape lemma
Weyl algebra

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10.1016/j.jalgebra.2026.01.014

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title = "Yet another differential shape lemma",

abstract = "Recently, Kauers, Koutschan, and Verron proved a non-commutative version of the classical shape lemma in the theory of Gr{\"o}bner bases. Their result requires the ideal to be D-radical. In this note, we prove a new non-commutative shape lemma that does not require this assumption.",

keywords = "Differential operators, Gr{\"o}bner basis, Shape lemma, Weyl algebra",

author = "\{van der Hoeven\}, Joris and Gleb Pogudin",

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year = "2026",

month = may,

day = "1",

doi = "10.1016/j.jalgebra.2026.01.014",

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T1 - Yet another differential shape lemma

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AU - Pogudin, Gleb

PY - 2026/5/1

Y1 - 2026/5/1

N2 - Recently, Kauers, Koutschan, and Verron proved a non-commutative version of the classical shape lemma in the theory of Gröbner bases. Their result requires the ideal to be D-radical. In this note, we prove a new non-commutative shape lemma that does not require this assumption.

AB - Recently, Kauers, Koutschan, and Verron proved a non-commutative version of the classical shape lemma in the theory of Gröbner bases. Their result requires the ideal to be D-radical. In this note, we prove a new non-commutative shape lemma that does not require this assumption.

KW - Differential operators

KW - Gröbner basis

KW - Shape lemma

KW - Weyl algebra

UR - https://www.scopus.com/pages/publications/105028410139

U2 - 10.1016/j.jalgebra.2026.01.014

DO - 10.1016/j.jalgebra.2026.01.014

M3 - Article

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SN - 0021-8693

VL - 693

SP - 683

EP - 689

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Yet another differential shape lemma

Abstract

Keywords

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