In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg I = reg I ; (c) arithdeg I = indeg I + 1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in ca...

In this paper we present a combinatorial study of binomial ideals of dimension 1 of k[X1, . . . , Xn], using monomial parametrizations of the irreducible affine curves defined by their associated primes. We find an algorithm that checks whether or not the ideal of a union of monomial curves is binomial and another one that calculates curves such that their associated ideal is a prescribed latti...

In this paper we consider diierent involutive divisions and describe their implementation in Mathematica together with algorithms for the construction of involutive bases for monomial ideals. As a straightforward application, we consider computation of the Hilbert function and the Hilbert polynomial for a monomial ideal, or for a polynomial one represented by its Grr obner basis. This allows on...

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

Let I be a monomial squarefree ideal of a polynomial ring S over a field K such that the sum of every three different ideals of its minimal prime ideals is the maximal ideal of S, or more generally a constant ideal. We associate to I a graph on [s], s = |MinS/I|, on which we may read the depth of I. In particular, depthS I does not depend on char K. Also we show that I satisfies Stanley’s Conje...

Alexander duality is made into a functor which extends the notion for monomial ideals to any finitely generated N-graded module. The functors associated with Alexander duality provide a duality on the level of free and injective resolutions, and numerous Bass and Betti number relations result as corollaries. A minimal injective resolution of a module M is equivalent to the injective resolution ...

We express the Segre class of a monomial scheme in projective space in terms of log canonical thresholds of associated ideals. Explicit instances of the relation amount to identities involving the classical polygamma functions.

An equigenerated monomial ideal [Formula: see text] in the polynomial ring is a Freiman if text], where analytic spread of and least number generators text]. In this paper, we classify certain classes Borel-type ideals, including Borel ideals with multiple principal text]-Borel which are Freiman.

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.