Stanley-reisner Rings and the Radicals of Lattice Ideals
نویسندگان
چکیده
In this article we associate to every lattice ideal IL,ρ ⊂ K[x1, . . . , xm] a cone σ and a graph Gσ with vertices the minimal generators of the Stanley-Reisner ideal of σ. To every polynomial F we assign a subgraph Gσ(F ) of the graph Gσ. Every expression of the radical of IL,ρ, as a radical of an ideal generated by some polynomials F1, . . . , Fs gives a spanning subgraph of Gσ, the ∪ s i=1Gσ(Fi). This result provides a lower bound for the minimal number of generators of IL,ρ and therefore improves the generalized Krull’s principal ideal theorem for lattice ideals. But mainly it provides lower bounds for the binomial arithmetical rank and the A-homogeneous arithmetical rank of a lattice ideal. Finally we show, by a family of examples, that the bounds given are sharp.
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