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Asymptotic
behavior of differential powers
Jennifer Kenkel, Lillian McPherson, Janet Page, Daniel Smolkin, Monroe Stephenson and Fuxiang Yang |
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Vol. 19 (2026), No. 2, 207–232
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Abstract |
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We study the differential power operation on ideals, recently defined in a work of Dao et al. (2018). We begin with a focus on monomial ideals in characteristic 0 and find a class of ideals whose differential powers are eventually principal. We also study the containment problem between ordinary and differential powers of ideals, in analogy to earlier work comparing ordinary and symbolic powers of ideals. We further define a possible closure operation on ideals, called the differential closure, in analogy with integral closure and tight closure. We show that this closure operation agrees with taking the radical of an ideal if and only if the ambient ring is a simple -module. |
Keywords
commutative algebra, monomial ideal, differential powers,
symbolic powers
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Mathematical Subject Classification
Primary: 13A15, 13N10
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Milestones
Received: 6 June 2023
Revised: 21 October 2024
Accepted: 23 October 2024
Published: 8 March 2026
Communicated by Vadim Ponomarenko
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Authors |
| Jennifer Kenkel | |
| Grinnell College Noyce Science Center Grinnell, IA United States |
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| Lillian McPherson | |
| University of California San
Diego La Jolla, CA United States |
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| Janet Page | |
| Mathematics Department North Dakota State University Fargo, ND United States |
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| Daniel Smolkin | |
| Ann Arbor, MI United States |
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| Monroe Stephenson | |
| Berlin Mathematical School Berlin Germany |
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| Fuxiang Yang | |
| University of Notre Dame Notre Dame, IN United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
