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We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals associated to numerical semigroups. This correspondence is shown to preserve the complete intersection property, and allows us to use some available algorithms to determine whether a given vanishing ideal is a complete intersection. We give formulae for the degree, and for the index of regularity of a complete intersection in terms of the Frobenius number and the generators of a numerical semigroup.
We characterize the graphs $G$ for which their toric ideals $I_G$ are complete intersections. In particular we prove that for a connected graph $G$ such that $I_G$ is complete intersection all of its blocks are bipartite except of at most two. We pro
In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of $bz^noplus T$ with no invertible elements, where $T$ is a finite abelian group. We also ch
Our purpose is to study the family of simple undirected graphs whose toric ideal is a complete intersection from both an algorithmic and a combinatorial point of view. We obtain a polynomial time algorithm that, given a graph $G$, checks whether its
The first goal of the present paper is to study the class groups of the edge rings of complete multipartite graphs, denoted by $Bbbk[K_{r_1,ldots,r_n}]$, where $1 leq r_1 leq cdots leq r_n$. More concretely, we prove that the class group of $Bbbk[K_{
We give a two step method to study certain questions regarding associated graded module of a Cohen-Macaulay (CM) module $M$ w.r.t an $mathfrak{m}$-primary ideal $mathfrak{a}$ in a complete Noetherian local ring $(A,mathfrak{m})$. The first step, we c