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Jag forskar huvudsakligen inom kommutativ algebra och homologisk algebra. Har fuskat ibland inom ickekommutativ algebra och kombinatorik.

I urval från Stockholms universitets publikationsdatabas

• Some comments to a result by Moreno

  2021. Ralf Fröberg. Communications in Algebra

  Artikel

  Moreno 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.

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• Algebraic relations among harmonic moments of plane polygons and their conjugates

  2020. Ralf Fröberg, Boris Shapiro, Y. Burman. International mathematics research notices 394

  Artikel

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• Primary Decomposition of Powers of the Prime Ideal of a Numerical Semigroup Ring

  2019. Ralf Fröberg.

  Artikel

  Let R=k[t(n1),...t(ns)] = k[x(1),...x(s)]/P be a numerical semigroup ring and let P-(n) = (PRP)-R-n boolean AND R be the symbolic power of P and R-s(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 non-Noetherian symbolic Rees rings for 3-generated semigroups. We determine the primary decomposition of powers of P for some classes of 3-generated numerical semigroups.

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• Algebraic Stories from One and from the Other Pockets

  2018. Ralf Fröberg (et al.).

  Artikel

  In 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.

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• 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, 1-14

  Artikel

  Given 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 I-k be, i.e., how small can the Hilbert function of C[x(1), ... , x(n)] / I-k 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/I-k, where I is the ideal generated by the d'th powers of the variables.

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• Questions and conjectures on extremal Hilbert series

  2018. Ralf Fröberg, Samuel Lundqvist. Revista de la Unión Matemática Argentina 59 (2), 415-429

  Artikel

  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. 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.

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• On Vandermonde Varieties

  2016. Ralf Fröberg, Boris Shapiro. Mathematica Scandinavica 119 (1), 73-91

  Artikel

  Motivated by the famous Skolem-Mahler-Lech 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 non-trivial 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.

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• On free resolutions of some semigroup rings

  2014. Valentina Barucci, Ralf Fröberg, Mesut Sahin. Journal of Pure and Applied Algebra 218 (6), 1107-1116

  Artikel

  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 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.

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• On differential operators of numerical semigroup rings

  2013. Valentina Barucci, Ralf Fröberg. Journal of Pure and Applied Algebra 217 (2), 230-237

  Artikel

  If 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 so-called 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).

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• Poincare series of some hypergraph algebras

  2013. Ralf Fröberg (et al.). Mathematica Scandinavica 112, 5-10

  Artikel

  A hypergraph H = (V, E), where V = {x(1),...,x(n)} and E subset of 2(V) defines a hypergraph algebra R-H = k[x(1),...,x(n)]/(x(i1)...x(ik); {i(1),...,i(k)} is an element of E). All our hypergraphs are d-uniform, i.e., vertical bar e(i)vertical bar = d for all e(i) is an element of E. We determine the Poincare series P-RH (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.

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• 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), 5600-5602

  Artikel

  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 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) k-th powers of homogeneous polynomials in C[x(0),x(1),...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.

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• Associated graded rings of one-dimensional analytically irreducible rings II

  2011. Valentina Barucci, Ralf Fröberg. Journal of Algebra 336 (1), 279-285

  Artikel

  Lance 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.

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• Associated graded rings of one-dimensional analytically irreducible rings

  2006. Valentina Barucci, Ralf Fröberg. Journal of Algebra 304 (1), 349-358

  Artikel

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• The Apery algorithm for a plane singularity with two branches

  2005. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Beiträge zu Algebra und Geometrie 46

  Artikel

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• The Hilbert series of the clique complex

  2005. Ralf Fröberg, Daniela Ferrarello. Graphs and combinatorics 21

  Artikel

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• The Hilbert series of the clique complex

  2005. Ralf Fröberg. Graphs and Combinatorics 21 (4), 401-405

  Artikel

  For a graph G, we show a theorem that establishes a correspondence between the fine Hilbert series of the Stanley-Reisner 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.

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• The Poincare series of the module of derivations of an affine monomial curve

  2004. Ralf Fröberg, Vincenzo Micale. J. Algebra 280

  Artikel

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• Arf characters of an algebroid curve

  2003. Ralf Fröberg, Valentina Barucci, Marco D'Anna. JP J. Algebra, Number theory and applications 3

  Artikel

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• On plane algebroid curves

  2002. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Commutative ring theory

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• Koszul homology and Lie algebras with application to generic forms and points

  2001. Ralf Fröberg, Clas Löfwall. Homology, homotopy and apllications 4

  Artikel

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• Normal Hilbert functions of one-dimensional local rings

  2001. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Comm. in Algebra 29

  Artikel

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• On the number of ideals of finite colength

  2001. Ralf Fröberg, Valentina Barucci. Lect. Notes in Pure and Appl. Math. 217

  Artikel

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• An affine monomial curve with irrational Poincare-Betti series

  2000. Ralf Fröberg, Jan-Erik Roos. J. Pure Appl. Algebra 152

  Artikel

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• Analytically unramified one-dimensional semilocal rings and their value semigroup

  2000. Ralf Fröberg, Valentina Barucci, Marco D'Anna. J. Pure Appl. Algebra 147

  Artikel

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• The semigroup of values of a one-dimensional local ring with two minimal primes

  2000. Ralf Fröberg, Valentina Barucci, Marco D'Anna. Comm. in Algebra 28

  Artikel

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• One-dimensional almost Gorenstein rings

  1997. Ralf Fröberg, Valentina Barucci. J. Algebra 188

  Artikel

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• Some comments on a paper by Moreno

  1997. Ralf Fröberg, Joakim Hollman.

  Rapport

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• A note on a paper by Miyazaki

  1994. Ralf Fröberg. Math. Scand. 77

  Artikel

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• Hilbert series for ideals generated by generic forms

  1994. Ralf Fröberg, Joakim Hollman. J. Symbolic Comp. 17

  Artikel

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• Methods to divide out certain solutions from systems of algebraic equations, applied to find all cyclic 8-roots

  1994. Ralf Fröberg, Göran Björck. Analysis, algebra, and computers in mathematical research (Luleå, 1992), 57-70

  Konferens

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• A characterization of k-trees

  1992. Ralf Fröberg. Discrete Math. 104

  Artikel

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• Segre products and Rees algebras of face rings

  1992. Ralf Fröberg, Le Hoa. Comm. in Algebra 20

  Artikel

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• How we proved that there are exactly 924 cyclic 7-roots

  1991. Ralf Fröberg, Jörgen Backelin. Proc. ISSAC-91

  Artikel

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• On Hilbert series for commutative and noncommutative graded algebras

  1991. Ralf Fröberg, Clas Löfwall. J. Pure Appl. Algebra 76

  Artikel

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• On Stanley-Reisner rings

  1990. Ralf Fröberg. Topics in algebra, Banach Center Publ. 26 (2)

  Artikel

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• A note on the Stanley-Reisner ring of a join and of a suspension

  1988. Ralf Fröberg. Manuscripta Math. 60

  Artikel

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• Gorenstein rings as maximal subrings of k[[x]] with fixed conductor

  1988. Ralf Fröberg, Christian Gottlieb, Roland Häggkvist. Comm. in Algebra 16

  Artikel

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• Connections between a local ring and its associated graded

  1987. Ralf Fröberg. J. Algebra 111

  Artikel

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• On numerical semigroups

  1987. Ralf Fröberg, Christian Gottlieb, Roland Häggkvist. Semigroup Forum 35

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• An inequality for Hilbert series of graded algebras

  1985. Ralf Fröberg. Math. Scand. 56

  Artikel

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• Koszul algebras, Veronese subrings, and rings with linear resolutions

  1985. Ralf Fröberg, Jörgen Backelin. Rev. Roumaine 30

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• Poincare series of short Artinian rings

  1985. Ralf Fröberg, Jörgen Backelin. J. Algebra 96

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• Rings with monomial relations having linear resolutions

  1985. Ralf Fröberg. J.pure Appl. Algebra 38

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• Compressed algebras

  1983. Ralf Fröberg, Dan Laksov. Springer Lect. Notes in math (1092)

  Artikel

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• Flat families of local artinian k-algebras with infinitely many Poincare series

  1983. Ralf Fröberg, Tor Gulliksen, Clas Löfwall. Springer Lecture Notes in math. 1183

  Artikel

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• A study of graded extremal rings and of monomial rings

  1982. Ralf Fröberg. Math. Scand. 51

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• Some complex constructions with applications to Poincare series

  1978. Ralf Fröberg. Springer Lecture Notes in math. 740

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• Determination of a class of Poincare series

  1975. Ralf Fröberg. Math. Scand. 37

  Artikel

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