Lifting Gröbner Bases from the Exterior Algebra
Andreas Nilsson, Jan Snellman · Communications in Algebra · 2003
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.