The Eliahou-Kervaire resolution over a skew polynomial ring




Ferraro, Luigi
Hardesty, Alexis

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Taylor & Francis


In a 1987 paper, Eliahou and Kervaire constructed a minimal resolution of a class of monomial ideals in a polynomial ring, called stable ideals. As a consequence of their construction they deduced several homological properties of stable ideals. Furthermore they showed that this resolution admits an associative, graded commutative product that satisfies the Leibniz rule. In this paper we show that their construction can be extended to stable ideals in skew polynomial rings. As a consequence we show that the homological properties of stable ideals proved by Eliahou and Kervaire hold also for stable ideals in skew polynomial rings.


Article originally published by Communications in Algebra, 1–27. English. Published 2023.
File has been archived under a 12-month publisher-required embargo. File will become available October 1, 2024.


Eliahou-Kervaire resolution, Minimal free resolutions, Monomial ideals, Skew polynomial rings, Stable ideals


This is the post-print version of an article that is available at Recommended citation: Ferraro, L., & Hardesty, A. (2023). The Eliahou-Kervaire resolution over a skew polynomial ring. Communications in Algebra, 1–27. This item has been deposited in accordance with publisher copyright and licensing terms and with the author’s permission.