Primary Decomposition with Differential Operators
Commutative Algebra
2022-06-08 v3 Algebraic Geometry
Analysis of PDEs
Abstract
We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minimal differential primary decompositions are unique up to change of bases. Our results generalize the construction of Noetherian operators for primary ideals in the analytic theory of Ehrenpreis-Palamodov, and they offer a concise method for representing affine schemes. The case of modules is also addressed. We implemented an algorithm in Macaulay2 that computes the minimal decomposition for an ideal in a polynomial ring.
Cite
@article{arxiv.2101.03643,
title = {Primary Decomposition with Differential Operators},
author = {Yairon Cid-Ruiz and Bernd Sturmfels},
journal= {arXiv preprint arXiv:2101.03643},
year = {2022}
}
Comments
to appear in International Mathematics Research Notices