digestive-tract 发表于 2025-3-21 19:17:32
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Paula Chakravartty,Katharine Sarikakis of a monomial ideal (over a polynomial ring) was posed by Kaplansky in the early 1960’s. Despite the helpful combinatorial structure of monomial ideals, the problem turned out to be hard. The structure of a minimal free monomial resolution can be quite complex. There exists a minimal free monomialExplicate 发表于 2025-3-22 05:38:52
Graded Free Resolutions,ule was introduced in two famous papers by Hilbert in ., .. Free resolutions provide a method for describing the structure of modules. There are several challenging and exciting conjectures involving resolutions. A number of open problems on graded syzygies and Hilbert functions are listed in a papehypnotic 发表于 2025-3-22 11:16:40
Hilbert Functions,graded components of the ideal..The Hilbert function encodes important information (for example, dimension and multiplicity). Hilbert’s insight was that it is determined by finitely many of its values..In many recent papers and books, Hilbert functions are studied using clever computations with binoRingworm 发表于 2025-3-22 16:09:56
Monomial Resolutions, of a monomial ideal (over a polynomial ring) was posed by Kaplansky in the early 1960’s. Despite the helpful combinatorial structure of monomial ideals, the problem turned out to be hard. The structure of a minimal free monomial resolution can be quite complex. There exists a minimal free monomialRingworm 发表于 2025-3-22 19:30:58
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Paula Chakravartty,Katharine Sarikakisn this situation, the guideline is to introduce new ideas and constructions which either have strong applications or/and are beautiful. Most proofs about monomial resolutions are easy. The key point is not to provide complicated proofs, but to introduce new beautiful ideas.有法律效应 发表于 2025-3-23 08:07:21
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