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We consider classes of ideals which generalize the mixed product ideals introduced by Restuccia and Villarreal, and also generalize the expansion construction by Bayati and the first author cite{BH}. We compute the minimal graded free resolution of generalized mixed product ideals and show that the regularity of a generalized mixed product ideal coincides with regularity of the monomial ideal by which it is induced.
This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Grobner basis can be computed by studying paths in
We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo-Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by $m(G)+1$, where $m(G)$ is t
Let $k$ be a field, $ mathcal{L}subset mathbb{Z}^n$ be a lattice such that $Lcap mathbb{N}^n={{bf 0}}$, and $I_Lsubset Bbbk[x_1,..., x_n]$ the corresponding lattice ideal. We present the generalized Scarf complex of $I_L$ and show that it is indispen
We introduce a notion of generalized local cohomology modules with respect to a pair of ideals $(I,J)$ which is a generalization of the concept of local cohomology modules with respect to $(I,J).$ We show that generalized local cohomology modules $
Let I be either the ideal of maximal minors or the ideal of 2-minors of a row graded or column graded matrix of linear forms L. In two previous papers we showed that I is a Cartwright-Sturmfels ideal, that is, the multigraded generic initial ideal gi