Ralf Fröberg
About me
The email I use is frobergralf at gmail.com
Teaching
No teaching
Research
My research is mainly in commutative and homological algebra. Have cheated in
sometimes noncommutative algebra and combinatorics
Publications
A selection from Stockholm University publication database

Some comments to a result by Moreno
2021. Ralf Fröberg. Communications in Algebra
ArticleMoreno studies the following question. Let I be an ideal in k[x(1), ... , x(n)] generated minimally by elements of degree d, d+1, d+2, .. .How long can such a sequence of generators be? Later he also studies the opposite question.

Algebraic relations among harmonic moments of plane polygons and their conjugates
2020. Ralf Fröberg, Boris Shapiro, Y. Burman. International mathematics research notices 394
Article 
Primary Decomposition of Powers of the Prime Ideal of a Numerical Semigroup Ring
2019. Ralf Fröberg.
ArticleLet R=k[t(n1),...t(ns)] = k[x(1),...x(s)]/P be a numerical semigroup ring and let P(n) = (PRP)Rn boolean AND R be the symbolic power of P and Rs(P) = circle plus(i >= 0)P((n))t(n) the symbolic Rees ring of P. It is hard to determine symbolic powers of P; there are even nonNoetherian symbolic Rees rings for 3generated semigroups. We determine the primary decomposition of powers of P for some classes of 3generated numerical semigroups.

Algebraic Stories from One and from the Other Pockets
2018. Ralf Fröberg (et al.).
ArticleIn what follows, we present a large number of questions which were posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014—Spring 2017 along with a number of results related to these problems. Many of the results were obtained by participants of the latter seminar.

Powers of generic ideals and the weak Lefschetz property for powers of some monomial complet intersections
2018. Mats Boij, Ralf Fröberg, Samuel Lundqvist. Journal of Algebra 495, 114
ArticleGiven an ideal I = (f(1) ... , f(r)) in C[x(1), ... , x(n),] generated by forms of degree d, and an integer k > 1, how large can the ideal Ik be, i.e., how small can the Hilbert function of C[x(1), ... , x(n)] / Ik be? If r <= n the smallest Hilbert function is achieved by any complete intersection, but for r > n, the question is in general very hard to answer. We study the problem for r = n + 1, where the result is known for k = 1. We also study a closely related problem, the Weak Lefschetz property, for S/Ik, where I is the ideal generated by the d'th powers of the variables.

Questions and conjectures on extremal Hilbert series
2018. Ralf Fröberg, Samuel Lundqvist. Revista de la Unión Matemática Argentina 59 (2), 415429
ArticleGiven 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. We concentrate on the minimal Hilbertseries, which is achieved when the forms are generic. In the polynomial ring we also consider the opposite case of maximal series. This is mainly a survey article, but we give a lot of problems and conjectures. The only novel results concern the maximal series in the polynomial ring.

On Vandermonde Varieties
2016. Ralf Fröberg, Boris Shapiro. Mathematica Scandinavica 119 (1), 7391
ArticleMotivated by the famous SkolemMahlerLech theorem we initiate in this paper the study of a natural class of determinantal varieties, which we call Vandermonde varieties. They are closely related to the varieties consisting of all linear recurrence relations of a given order possessing a nontrivial solution vanishing at a given set of integers. In the regular case, i.e., when the dimension of a Vandermonde variety is the expected one, we present its free resolution, obtain its degree and the Hilbert series. Some interesting relations among Schur polynomials are derived. Many open problems and conjectures are posed.

On free resolutions of some semigroup rings
2014. Valentina Barucci, Ralf Fröberg, Mesut Sahin. Journal of Pure and Applied Algebra 218 (6), 11071116
ArticleFor some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results by giving the whole graded minimal free resolutions explicitly. Then we use these resolutions to determine some invariants of the semigroups and certain interesting relations among them. Finally, we determine semigroups of small embedding dimensions which have strongly indispensable resolutions.

On differential operators of numerical semigroup rings
2013. Valentina Barucci, Ralf Fröberg. Journal of Pure and Applied Algebra 217 (2), 230237
ArticleIf S = < d(1),...,d(nu)> is a numerical semigroup, we call the ring C[S] = C[t(d1),...,t(d nu)] the semigroup ring of S. We study the ring of differential operators on C[S] , and its associated graded in the filtration induced by the order of the differential operators. We find that these are easy to describe if S is a socalled Art semigroup. If I is an ideal in C[S] that is generated by monomials, we also give some results on Der(I, I) (the set of derivations which map I into I).

Poincare series of some hypergraph algebras
2013. Ralf Fröberg (et al.). Mathematica Scandinavica 112, 510
ArticleA hypergraph H = (V, E), where V = {x(1),...,x(n)} and E subset of 2(V) defines a hypergraph algebra RH = k[x(1),...,x(n)]/(x(i1)...x(ik); {i(1),...,i(k)} is an element of E). All our hypergraphs are duniform, i.e., vertical bar e(i)vertical bar = d for all e(i) is an element of E. We determine the Poincare series PRH (t) = Sigma(infinity)(i=1) dim(k) Tor(i)(RH) (k, k)(t)(i) for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincare series of the graph algebra of the wheel graph.

On the Waring problem for polynomial rings
2012. Ralf Fröberg, Giorgio Ottaviani, Boris Shapiro. Proceedings of the National Academy of Sciences of the United States of America 109 (15), 56005602
ArticleIn 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 is an element of C[x(0),x(1),..,x(n)] of degree divisible by k >= 2 can be represented as a sum of at most k(n) kth powers of homogeneous polynomials in C[x(0),x(1),...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.

Associated graded rings of onedimensional analytically irreducible rings II
2011. Valentina Barucci, Ralf Fröberg. Journal of Algebra 336 (1), 279285
ArticleLance Bryant noticed in his thesis (Bryant, 2009 [3]), that there was a flaw in our paper (Barucci and Froberg, 2006 (2]). It can be fixed by adding a condition, called the BF condition in Bryant (2009) [3]. We discuss some equivalent conditions, and show that they are fulfilled for some classes of rings, in particular for our motivating example of semigroup rings. Furthermore we discuss the connection to a similar result, stated in more generality, by Cortadellas and Zarzuela in [4]. Finally we use our result to conclude when a semigroup ring in embedding dimension at most three has an associated graded which is a complete intersection.

Associated graded rings of onedimensional analytically irreducible rings
2006. Valentina Barucci, Ralf Fröberg. Journal of Algebra 304 (1), 349358
Article 
The Apery algorithm for a plane singularity with two branches
2005. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Beiträge zu Algebra und Geometrie 46
Article 
The Hilbert series of the clique complex
2005. Ralf Fröberg, Daniela Ferrarello. Graphs and combinatorics 21
Article 
The Hilbert series of the clique complex
2005. Ralf Fröberg. Graphs and Combinatorics 21 (4), 401405
ArticleFor a graph G, we show a theorem that establishes a correspondence between the fine Hilbert series of the StanleyReisner ring of the clique complex for the complementary graph of G and the fine subgraph polynomial of G. We obtain from this theorem some corollaries regarding the independent set complex and the matching complex.

The Poincare series of the module of derivations of an affine monomial curve
2004. Ralf Fröberg, Vincenzo Micale. J. Algebra 280
Article 
Arf characters of an algebroid curve
2003. Ralf Fröberg, Valentina Barucci, Marco D'Anna. JP J. Algebra, Number theory and applications 3
Article 
On plane algebroid curves
2002. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Commutative ring theory
Article 
Koszul homology and Lie algebras with application to generic forms and points
2001. Ralf Fröberg, Clas Löfwall. Homology, homotopy and apllications 4
Article 
Normal Hilbert functions of onedimensional local rings
2001. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Comm. in Algebra 29
Article 
On the number of ideals of finite colength
2001. Ralf Fröberg, Valentina Barucci. Lect. Notes in Pure and Appl. Math. 217
Article 
An affine monomial curve with irrational PoincareBetti series
2000. Ralf Fröberg, JanErik Roos. J. Pure Appl. Algebra 152
Article 
Analytically unramified onedimensional semilocal rings and their value semigroup
2000. Ralf Fröberg, Valentina Barucci, Marco D'Anna. J. Pure Appl. Algebra 147
Article 
The semigroup of values of a onedimensional local ring with two minimal primes
2000. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Comm. in Algebra 28
Article 
Onedimensional almost Gorenstein rings
1997. Ralf Fröberg, Valentina Barucci. J. Algebra 188
Article 
Some comments on a paper by Moreno
1997. Ralf Fröberg, Joakim Hollman.
Report 
A note on a paper by Miyazaki
1994. Ralf Fröberg. Math. Scand. 77
Article 
Hilbert series for ideals generated by generic forms
1994. Ralf Fröberg, Joakim Hollman. J. Symbolic Comp. 17
Article 
Methods to divide out certain solutions from systems of algebraic equations, applied to find all cyclic 8roots
1994. Ralf Fröberg, Göran Björck. Analysis, algebra, and computers in mathematical research (Luleå, 1992), 5770
Conference 
A characterization of ktrees
1992. Ralf Fröberg. Discrete Math. 104
Article 
Segre products and Rees algebras of face rings
1992. Ralf Fröberg, Le Hoa. Comm. in Algebra 20
Article 
How we proved that there are exactly 924 cyclic 7roots
1991. Ralf Fröberg, Jörgen Backelin. Proc. ISSAC91
Article 
On Hilbert series for commutative and noncommutative graded algebras
1991. Ralf Fröberg, Clas Löfwall. J. Pure Appl. Algebra 76
Article 
On StanleyReisner rings
1990. Ralf Fröberg. Topics in algebra, Banach Center Publ. 26 (2)
Article 
A note on the StanleyReisner ring of a join and of a suspension
1988. Ralf Fröberg. Manuscripta Math. 60
Article 
Gorenstein rings as maximal subrings of k[[x]] with fixed conductor
1988. Ralf Fröberg, Christian Gottlieb, Roland Häggkvist. Comm. in Algebra 16
Article 
Connections between a local ring and its associated graded
1987. Ralf Fröberg. J. Algebra 111
Article 
On numerical semigroups
1987. Ralf Fröberg, Christian Gottlieb, Roland Häggkvist. Semigroup Forum 35
Article 
An inequality for Hilbert series of graded algebras
1985. Ralf Fröberg. Math. Scand. 56
Article 
Koszul algebras, Veronese subrings, and rings with linear resolutions
1985. Ralf Fröberg, Jörgen Backelin. Rev. Roumaine 30
Article 
Poincare series of short Artinian rings
1985. Ralf Fröberg, Jörgen Backelin. J. Algebra 96
Article 
Rings with monomial relations having linear resolutions
1985. Ralf Fröberg. J.pure Appl. Algebra 38
Article 
Compressed algebras
1983. Ralf Fröberg, Dan Laksov. Springer Lect. Notes in math (1092)
Article 
Flat families of local artinian kalgebras with infinitely many Poincare series
1983. Ralf Fröberg, Tor Gulliksen, Clas Löfwall. Springer Lecture Notes in math. 1183
Article 
A study of graded extremal rings and of monomial rings
1982. Ralf Fröberg. Math. Scand. 51
Article 
Some complex constructions with applications to Poincare series
1978. Ralf Fröberg. Springer Lecture Notes in math. 740
Article 
Determination of a class of Poincare series
1975. Ralf Fröberg. Math. Scand. 37
Article
Show all publications by Ralf Fröberg at Stockholm University