The Eliahou-Kervaire resolution over a skew polynomial ring
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917585213194240 |
|---|---|
| author | Ferraro, Luigi Hardesty, Alexis |
| author_facet | Ferraro, Luigi Hardesty, Alexis |
| contents | 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. Finally we show that the resolution we construct admits a product generalizing the one given by Eliahou and Kervaire in the commutative case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_05812 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Eliahou-Kervaire resolution over a skew polynomial ring Ferraro, Luigi Hardesty, Alexis Rings and Algebras Commutative Algebra Quantum Algebra 16E05, 16E45 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. Finally we show that the resolution we construct admits a product generalizing the one given by Eliahou and Kervaire in the commutative case. |
| title | The Eliahou-Kervaire resolution over a skew polynomial ring |
| topic | Rings and Algebras Commutative Algebra Quantum Algebra 16E05, 16E45 |
| url | https://arxiv.org/abs/2108.05812 |