Cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals. (English) Zbl 07911008
Summary: We prove that the Pommaret-Seiler resolution for quasi-stable ideals is cellular and give a cellular structure for it. This shows that this resolution is a generalization of the well known Eliahou-Kervaire resolution for stable ideals in a deeper sense. We also prove that the Pommaret-Seiler resolution can be reduced to the minimal one via Discrete Morse Theory and provide a constructive algorithm to perform this reduction.
MSC:
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
| 05E40 | Combinatorial aspects of commutative algebra |
Keywords:
quasi-stable ideals; Pommaret bases; Pommaret-Seiler resolution; cellular resolutions; discrete Morse theoryReferences:
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