Complete Intersection Lattice Ideals

In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of \bz^n\oplus T with no invertible elements, where $T$ is a finite abelian group. We also characterize the lattice ideals that are set-theoretic complete intersections on binomials

Graver degrees are not polynomially bounded by true circuit degrees

Let $I_A$ be a toric ideal. We prove that the degrees of the elements of the Graver basis of $I_A$ are not polynomially bounded by the true degrees of the circuits of $I_A$.Comment: 8 pages, 1 figur

Minimal generators of toric ideals of graphs

Let $I_G$ be the toric ideal of a graph $G$. We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal $I_G$

Binomial generation of the radical of a lattice ideal

Let $I_{L, \rho}$ be a lattice ideal. We provide a necessary and sufficient criterion under which a set of binomials in $I_{L, \rho}$ generate the radical of $I_{L, \rho}$ up to radical. We apply our results to the problem of determining the minimal number of generators of $I_{L, \rho}$ or of the $rad(I_{L, \rho})$ up to radical.Comment: 14 pages, to appear in Journal of Algebr