Binomial arithmetical rank of lattice ideals

 In this paper, we will show that a lattice ideal is a complete intersection if and only if its binomial arithmetical rank equals its height, if the characteristic of the base field k is zero. And we will give the condition that a binomial ideal equals a lattice ideal up to radical in the case of char k=0. Further, we will study the upper bound of the binomial arithmetical rank of lattice ideals and give a sharp bound for the lattice ideals of codimension two. Received: 12 June 2001 / Revised version: 22 July 2002