Ideals Of Mixed Products Research Articles

Normality of Rees algebras of generalized mixed product ideals

Let $K$ be a field and $K[x_1,x_{2}]$ the polynomial ring in two
 variables over $K$ with each $x_i$ of degree $1$. Let $L$ be the
 generalized mixed product ideal induced by a monomial ideal
 $I\subset K[x_1,x_2]$, where the ideals substituting the monomials
 in $I$ are squarefree Veronese ideals. In this paper, we study the
 integral closure of $L$, and the normality of $\mathcal{R}(L)$, the
 Rees algebra of $L$. Furthermore, we give a geometric description of
 the integral closure of $\mathcal{R}(L)$.

On the Cohen-Macaulayness of Bracket Powers of Generalized Mixed Product Ideals

On the Cohen-Macaulayness of Bracket Powers of Generalized Mixed Product Ideals

The Jacobian Dual of Certain Mixed Product Ideals

We consider the symmetric algebra of a class of monomial ideals generated by s-sequences. For these ideals with linear syzygies, we determine their Jacobian dual modules and study their duality properties.

On the normality of generalized mixed product ideals

Let L be the generalized mixed product ideal induced by a monomial ideal I. We characterize the unmixed generalized mixed product ideals. Furthermore, we show that I is normal if and only if L is normal.

Algebraic and homological properties of generalized mixed product ideals

Algebraic and homological invariants of generalized mixed product ideals induced by a monomial ideal are studied. We characterize the Cohen–Macaulay generalized mixed product ideals.

The Stanley regularity of complete intersections and ideals of mixed products

Let [Formula: see text] be a polynomial ring over a field [Formula: see text] and [Formula: see text] a monomial ideal. We give some inequalities on Stanley regularity of monomial ideals. As consequences, we prove that [Formula: see text] and [Formula: see text] hold in the following cases: (1) [Formula: see text] is a complete intersection; (2) [Formula: see text] is an ideal of mixed products.

Sequentially Cohen-Macaulay Mixed Product Ideals

We classify the ideals of mixed products that are sequentially Cohen-Macaulay.

Stanley conjecture on monomial ideals of mixed products

It is proved that the Stanley conjecture holds for monomial ideals of mixed products, i.e., if $I$ is an ideal of mixed products in a polynomial ring $S$ over a field, then ${\rm sdepth}_S(I) \geq {\rm depth}_S(I)$ and ${\rm sdepth}_S(S/I) \geq {\rm depth}_S(S/I)$.

Generalized mixed product ideals

We consider classes of ideals which generalize the mixed product ideals introduced by Restuccia and Villarreal (see [5]), and also generalize the expansion construction by Bayati and Herzog [1]. 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 the regularity of the monomial ideal by which it is induced.

Mixed Product Ideals Generated by s-Sequences

We consider monomial ideals of mixed products in the polynomial ring in two sets of variables and we investigate when they are generated by an s-sequence in order to compute invariants of their symmetric algebra.

Betti numbers of mixed product ideals

We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products. Moreover when these ideals are Cohen-Macaulay we calculate their type.

Some algebraic invariants related to mixed product ideals

We compute some algebraic invariants (e.g. depth, Castelnuovo-Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products.

ON THE NORMALITY OF MONOMIAL IDEALS OF MIXED PRODUCTS

Let R = K[x, y] be a polynomial ring in two disjoint sets of variables x, y over a field K. We study ideals of mixed products L = IkJr + IsJt such that k + r = s + t, where Ik (resp. Jr ) denotes the ideal of R generated by the square-free monomials of degree k (resp. r) in the x (resp. y ) variables. Our main result is a characterization of when a given ideal L of mixed products is normal. *Partially supported by CONACyT grant 27931E and SNI, México.