Complete intersections in binomial and lattice ideals
  For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic complete intersections. In characteristic zero, we show that an arbitrary lattice ideal which is a binomial set theoretic complete intersection is a complete intersection. 
Hiram H. Lopez and Rafael H. Villarreal
math.AC