Binomial generation of the radical of a lattice ideal

Let $I_{L, ρ}$ be a lattice ideal. We provide a necessary and sufficient criterion under which a set of binomials in $I_{L, ρ}$ generate the radical of $I_{L, ρ}$ up to radical. We apply our results to the problem of determining the minimal number of generators of $I_{L, ρ}$ or of the $rad(I_{L, ρ})$ up to radical.

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