Lifting Grobner bases from the exterior algebra

Details Lifting Grobner bases from the exterior algebra Lifting Grobner bases from the exterior algebra

2000-10-12

arxiv.org/abs/math/0010117v2

Communications in Algebra, vol 31, issue 12, 2003, pp 5715 - 5725

Mathematics

Commutative Algebra

6 pages, LaTeX2e

Scientific paper

10.1081/AGB-120024850

In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra 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 notion of generic initial ideals in the free assoicative algebra, and show that gin's of ideals containing the commutator ideal, or the anti-commutator ideal, are finitely generated.

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