35 citations · 49 across the 12 of their papers we have counts for
13 papers
Generic forms
Ralf Fröberg, Clas Löfwall
We study forms , , in which is the free associative algebra or the polynomial ring , where …
Hilbert coefficients of quadratic algebras
Ralf Froberg
If is a graded artinian algebra, then the length of becomes a polynomial in of degree for large . If we write this polyno…
On Stanley-Reisner rings with linear resolution
Ralf Froberg
For a graph , Bayer-Denker-Milutinović-Rowlands-Sundaram-Xue study in \cite{B-D-M-R-S-X} a new graph complex , namely the simplicial complex with facets that are compl…
Ideals of generic forms
Ralf Froberg
We determine the Hilbert series of some classes of ideals generated by generic forms of degree two and three, and investigate the difference to the Hilbert series of ideals generat…
The graded Betti numbers of truncation of ideals in polynomial rings
Chwas Ahmed, Ralf Fröberg, Mohammed Rafiq Namiq
Let , a graded algebra satisfies if is generated in degree , and the graded minimal resolution is linear the first steps,…
Gorenstein rings generated by strongly stable sets of quadratic monomials
Ralf Fröberg, Lisa Nicklasson
We characterize all Gorenstein rings generated by strongly stable sets of monomials of degree two. We compute their Hilbert series in several cases, which also provides an answer t…
Algebraic stories from one and from the other pockets
Ralf Fröberg, Samuel Lundqvist, Alessandro Oneto +1
We present a number of questions in commutative algebra posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014 - Spring 2017.
Extremal Hilbert series
Ralf Fröberg, Samuel Lundqvist
Given an ideal of forms in an algebra (polynomial ring, tensor algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we consider the Hilbert series of the factor ring.…
Powers of generic ideals and the weak Lefschetz property for powers of some monomial complete intersections
Mats Boij, Ralf Fröberg, Samuel Lundqvist
Given an ideal in generated by forms of degree , and an integer , how large can the ideal be, i.e., how small can the…
On free resolutions of some semigroup rings
Valentina Barucci, Ralf Fröberg, Mesut Sahin
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has…
On the Waring problem for polynomial rings
Ralf Fröberg, Giorgio Ottaviani, Boris Shapiro
In this note we discuss an analog of the classical Waring problem for C[x_0, x_1,...,x_n]. Namely, we show that a general homogeneous polynomial p \in C[x_0,x_1,...,x_n] of degree…
On differential operators of numerical semigroup rings
Valentina Barucci, Ralf Fröberg
If is a numerical semigroup, we call the ring $\C[S]=\C[t^{d_1},...,t^{d_ν}]$ the semigroup ring of . We study the ring of differential operators on $\C[S]$, a…
Poincaré series of some hypergraph algebras
Eric Emtander, Ralf Fröberg, Fatemeh Mohammadi +1
A hypergraph , where and defines a hypergraph algebra . All our hypergr…