15 citations · 39 across the 12 of their papers we have counts for
12 papers
Ideals and their Fitting ideals
David Eisenbud, Antonino Ficarra, Jürgen Herzog +1
For an ideal in a Noetherian ring , the Fitting ideals are studied. We discuss the question of when or $\sqrt{\textrm{Fitt}_j(I)}…
The reduced divisor class group and the torsion number
Jürgen Herzog, Takayuki Hibi
The reduced divisor class group of a normal Cohen--Macaulay graded domain together with its torsion number is introduced. They are studied in detail especially for normal affine se…
Behaviour of the normalized depth function
Antonino Ficarra, Jürgen Herzog, Takayuki Hibi
Let be a squarefree monomial ideal, a field. The th squarefree power of is the monomial ideal of generated by all squarefree…
Binomial ideals attached to finite collections of cells
Jürgen Herzog, Takayuki Hibi, Somayeh Moradi
We consider the ideal of inner -minors of a finite set of cells , which we call the cell ideal of . A nice interpretation for the hei…
The regularity of edge rings and matching numbers
Jürgen Herzog, Takayuki Hibi
Let denote the edge ring of a finite connected simple graph on and $\mat(G)$ the matching number of . It is shown that $\reg(K[G]) \leq \mat(G)$ if is non-b…
Stability properties of powers of ideals over regular local rings of small dimension
Jürgen Herzog, Amir Mafi
Let be a regular local ring or a polynomial ring over a field, and let be an ideal of which we assume to be graded if is a polynomial ring. Let astab…
The face ideal of a simplicial complex
Jürgen Herzog, Takayuki Hibi
Given a simplicial complex we associate to it a squarefree monomial ideal which we call the face ideal of the simplicial complex, and show that it has linear quotients. It turns ou…
Linear flags and Koszul filtrations
Viviana Ene, Jürgen Herzog, Takayuki Hibi
We show that the graded maximal ideal of a graded -algebra has linear quotients for a suitable choice and order of its generators if the defining ideal of has a quadrati…
Polarization of Koszul cycles with applications to powers of edge ideals of whisker graphs
Jürgen Herzog, Takayuki Hibi, Ayesha Asloob Qureshi
In this paper, we introduced the polarization of Koszul cycles and use it to study the depth function of powers of edge ideals of whisker graphs.
Koszul binomial edge ideals
Viviana Ene, Jürgen Herzog, Takayuki Hibi
It is shown that if the binomial edge ideal of a graph defines a Koszul algebra, then must be chordal and claw free. A converse of this statement is proved for a class of c…
Bounding the socles of powers of squarefree monomial ideals
Jürgen Herzog, Takayuki Hibi
Let be the polynomial ring in variables over a field and a squarefree monomial ideal. In the present paper we are interested in the monom…
The possible extremal Betti numbers of a homogeneous ideal
Jürgen Herzog, Leila Sharifan, Matteo Varbaro
We give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of any homogeneous ideal in a polynomial ring over a field.