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

Computing the degree of a lattice ideal of dimension one

We show that the degree of a graded lattice ideal of dimension 1 is the order of the torsion subgroup of the quotient group of the lattice. This gives an efficient method to compute the degree of this type of lattice ideals.Comment: J. Symbolic Comput., to appea

Border bases for lattice ideals

The main ingredient to construct an O-border basis of an ideal I $\subseteq$ K[x1,. .., xn] is the order ideal O, which is a basis of the K-vector space K[x1,. .., xn]/I. In this paper we give a procedure to find all the possible order ideals associated with a lattice ideal IM (where M is a lattice of Z n). The construction can be applied to ideals of any dimension (not only zero-dimensional) and shows that the possible order ideals are always in a finite number. For lattice ideals of positive dimension we also show that, although a border basis is infinite, it can be defined in finite terms. Furthermore we give an example which proves that not all border bases of a lattice ideal come from Gr\"obner bases. Finally, we give a complete and explicit description of all the border bases for ideals IM in case M is a 2-dimensional lattice contained in Z 2 .Comment: 25 pages, 3 figures. Comments welcome!, MEGA'2015 (Special Issue), Jun 2015, Trento, Ital

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.Comment: Internat. J. Algebra Comput., to appea

Intuitionistic FWI-ideals of residuated lattice Wajsberg algebras

The notions of intutionistic fuzzy Wajsberg implicative ideal( –ideal) and intuitionistic fuzzy lattice ideal of residuated Wajsberg algebras are introduced. Also,  we show that every intuitionistic - ideal of residuated lattice Wajsberg algebra is an intuitionistic fuzzy lattice ideal of residuated lattice Wajsberg algebra. Further, we discuss its converse part