AbstractThe lifting problem for homogeneous ideals is studied. A relation between a homogeneous ideal J and its liftings is established using a syzygy basis of J. This relation is then used to obtain an algorithm for finding all the liftings of a homogeneous ideal. As an application of the algorithm, we discover the first example of a homogeneous ideal of dimension 0 in four variables which is not liftable to a radical ideal over the field of rational numbers
Abstract. Let k[x1,..., xn] be a polynomial ring in n variables, and let I ⊂ k[x1,..., xn] be a homo...
AbstractSuppose J is a closed ideal in a unital C*-algebra A. This paper reduces the problem of lift...
The goal of this paper is to present examples of families of homogeneous ideals in the polynomial r...
We study the locus of the liftings of a homogeneous ideal H in a polynomial ring over any field. W...
AbstractWe prove here that if k is a field of zero characteristic, then any homogenous ideal in k[X,...
AbstractWinkler (1988) and Pauer (1992) present algorithms for a Hensel lifting of a modular Gröbner...
By focusing our attention on the set of monomials outside a given monomial ideal, we tackle the stud...
Abstract. We show that there are a cardinal µ, a σ-ideal I ⊆ P(µ) and a σ-subalgebra B of subsets of...
AbstractIn 1977, Nicholson developed the theory of suitable rings (Trans. Amer. Math. Soc.229 (1977)...
In this paper we characterize the h-vector of a Gorenstein codimension three domain. Main tool is a ...
AbstractLet I be a perfect height 2 homogeneous ideal in a graded polynomial algebra over a field. B...
AbstractLet J be a strongly stable monomial ideal in S=K[x0,…,xn] and let Mf(J) be the family of all...
An ideal I in a ring R is called a lifting ideal if idempotents can be lifted modulo every left idea...
We prove in ZFC that for mu >= aleph_2 there is a sigma --ideal I on mu and a Boolean sigma --subalg...
AbstractWe define a family of homogeneous ideals with large projective dimension and regularity rela...
Abstract. Let k[x1,..., xn] be a polynomial ring in n variables, and let I ⊂ k[x1,..., xn] be a homo...
AbstractSuppose J is a closed ideal in a unital C*-algebra A. This paper reduces the problem of lift...
The goal of this paper is to present examples of families of homogeneous ideals in the polynomial r...
We study the locus of the liftings of a homogeneous ideal H in a polynomial ring over any field. W...
AbstractWe prove here that if k is a field of zero characteristic, then any homogenous ideal in k[X,...
AbstractWinkler (1988) and Pauer (1992) present algorithms for a Hensel lifting of a modular Gröbner...
By focusing our attention on the set of monomials outside a given monomial ideal, we tackle the stud...
Abstract. We show that there are a cardinal µ, a σ-ideal I ⊆ P(µ) and a σ-subalgebra B of subsets of...
AbstractIn 1977, Nicholson developed the theory of suitable rings (Trans. Amer. Math. Soc.229 (1977)...
In this paper we characterize the h-vector of a Gorenstein codimension three domain. Main tool is a ...
AbstractLet I be a perfect height 2 homogeneous ideal in a graded polynomial algebra over a field. B...
AbstractLet J be a strongly stable monomial ideal in S=K[x0,…,xn] and let Mf(J) be the family of all...
An ideal I in a ring R is called a lifting ideal if idempotents can be lifted modulo every left idea...
We prove in ZFC that for mu >= aleph_2 there is a sigma --ideal I on mu and a Boolean sigma --subalg...
AbstractWe define a family of homogeneous ideals with large projective dimension and regularity rela...
Abstract. Let k[x1,..., xn] be a polynomial ring in n variables, and let I ⊂ k[x1,..., xn] be a homo...
AbstractSuppose J is a closed ideal in a unital C*-algebra A. This paper reduces the problem of lift...
The goal of this paper is to present examples of families of homogeneous ideals in the polynomial r...
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