2000/10/18 by Andreas Nilsson, Jan Snellman
Computer Science · Mathematics · #Advanced Algebra and Logic #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #msc:13P10 #msc:15A75 #msc:16S15
paper · pdf · doi:10.1081/agb-120024850
published as Communications in Algebra, vol 31, issue 12, 2003, pp 5715 - 5725 · 6 pages, LaTeX2e
arxiv created 2000/10/18 · openalex publication_date 2003/01/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
Eisenbud et al. proved a number of results regarding Gröbner bases and initial ideals of those ideals J in the free associative algebra K ⟨X 1,…, X n ⟩ which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one weak notion of generic initial ideals in K ⟨X 1,…, X n ⟩, and show that generic initial ideals of ideals containing the anti-commutator ideal, or the commutator ideal, are finitely generated.