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  • 1.
    Bøgvad, Rikard
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Gonçalves, Iara
    Stockholm University, Faculty of Science, Department of Mathematics.
    Decomposition of perverse sheaves on plane line arrangements2018In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 46, no 6, p. 2476-2487Article in journal (Refereed)
    Abstract [en]

    On the complement X = C-2 - U-i=1(n) L-i to a central plane line arrangement U-i=1(n) L-i subset of C-2, a locally constant sheaf of complex vector spaces L-a is associated to any multi-index aC(n). Using the description of MacPherson and Vilonen of the category of perverse sheaves [7, 8], we obtain a criterion for the irreducibility and number of decomposition factors of the direct image j : x -> C-2 as a perverse sheaf, where j:XC2 is the canonical inclusion.

  • 2. Carlini, Enrico
    et al.
    Oneto, Alessandro
    Stockholm University, Faculty of Science, Department of Mathematics. Polytechnic University of Turin, Italy.
    Monomials as Sums of k-th Powers of Forms2015In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, no 2, p. 650-658Article in journal (Refereed)
    Abstract [en]

    Motivated by recent results on the Waring problem for polynomial rings [4] and representation of monomial as sum of powers of linear forms [3], we consider the problem of presenting monomials of degree kd as sums of kth-powers of forms of degree d. We produce a general bound on the number of summands for any number of variables which we refine in the two variables case. We completely solve the k = 3 case for monomials in two and three variables.

  • 3.
    Emtander, Eric
    Stockholm University, Faculty of Science, Department of Mathematics.
    Betti numbers of hypergraphs2009In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 37, no 5, p. 1545-1571Article in journal (Refereed)
    Abstract [en]

    In this article, we study some algebraic properties of hypergraphs, in particular their Betti numbers. We define some different types of complete hypergraphs, which to the best of our knowledge are not previously considered in the literature. Also, in a natural way, we define a product on hypergraphs, which in a sense is dual to the join operation on simplicial complexes. For such product, we give a general formula for the Betti numbers, which specializes neatly in case of linear resolutions.

  • 4.
    Gottlieb, Christian
    Stockholm University, Faculty of Science, Department of Mathematics.
    A proof that commutative Artinian rings are Noetherian1995In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, no 12, p. 4687-4691Article in journal (Refereed)
  • 5.
    Gottlieb, Christian
    Stockholm University.
    An integer-valued function related to the number of generators of modules over local rings of small dimension1993In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 21, no 11, p. 4115-4118Article in journal (Refereed)
  • 6.
    Gottlieb, Christian
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bounding the number of generators for a class of ideals in local rings1995In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, no 4, p. 1499-1502Article in journal (Refereed)
  • 7.
    Gottlieb, Christian
    Stockholm University, Faculty of Science, Department of Mathematics.
    Finite unions of submodules2015In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, no 2, p. 847-855Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with finite unions of ideals and modules. The first main result is that, if N ⊆ N 1 ∪N 2 ∪ … ∪ N s is a covering of a module N by submodules N i , such that all but two of the N i are intersections of strongly irreducible modules, then N ⊆ N k for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on coverings by primary submodules. In the last section unions of cosets is studied.

  • 8.
    Gottlieb, Christian
    Stockholm University.
    Length and dimension modulo a Serre category1997In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 25, no 5, p. 1553-1561Article in journal (Refereed)
  • 9.
    Gottlieb, Christian
    Stockholm University.
    Modules covered by finite unions of submodules1998In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 26, no 7, p. 2351-2359Article in journal (Refereed)
  • 10.
    Gottlieb, Christian
    Stockholm University.
    On finite unions of ideals and cosets1994In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 22, no 8, p. 3087-3097Article in journal (Refereed)
  • 11.
    Gottlieb, Christian
    Stockholm University.
    On generators of ideals in one-dimensional local rings1993In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 21, no 2, p. 421-425Article in journal (Refereed)
  • 12.
    Gottlieb, Christian
    Stockholm University.
    On ideals which are almost zero, and related concepts1996In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 24, no 6, p. 2201-2209Article in journal (Refereed)
  • 13.
    Gottlieb, Christian
    Stockholm University, Faculty of Science, Department of Mathematics.
    The Nakayama Property of a Module and Related Concepts2015In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, no 12, p. 5131-5140Article in journal (Refereed)
    Abstract [en]

    Three related properties of a module are investigated in this article, namely the Nakayama property, the Maximal property, and the S-property. A module M has the Nakayamapropertyif aM=M for an ideal a implies that sM=0 for some s∈a+1. A module M has the Maximal property if there is in M a maximal proper submodule, and finally, M is said to have the S-property if S^{−1}M = 0 for a multiplicatively closed set S implies that sM=0 for some s∈S. 

  • 14.
    Löfwall, Clas
    Stockholm University, Faculty of Science, Department of Mathematics.
    DECOMPOSITION THEOREMS FOR A GENERALIZATION OF THE HOLONOMY LIE ALGEBRA OF AN ARRANGEMENT2016In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 44, no 11, p. 4654-4663Article in journal (Refereed)
    Abstract [en]

    In the article When does the Associated graded Lie algebra of an Arrangement Group Decompose? by Stefan Papadima and Alexander Suciu [7], it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through origin decomposes as a direct product of Lie algebras in degree at least two if and only if a certain (computable) condition is fulfilled. We prove similar results for a class of Lie algebras which is a generalization of the holonomy Lie algebras. The proof methods are the same as in the article cited above.

  • 15.
    Nicklasson, Lisa
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the Hilbert series of ideals generated by generic forms2017In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, no 8, p. 3390-3395Article in journal (Refereed)
    Abstract [en]

    There is a longstanding conjecture by Fröberg about the Hilbert series of the ring RI, where R is a polynomial ring, and I an ideal generated by generic forms. We prove this conjecture true in the case when I is generated by a large number of forms, all of the same degree. We also conjecture that an ideal generated by m’th powers of generic forms of degree d≥2 gives the same Hilbert series as an ideal generated by generic forms of degree md. We verify this in several cases. This also gives a proof of the first conjecture in some new cases.

  • 16.
    Tambour, Torbjörn
    Stockholm University.
    The number of solutions of some equations in finite groups and a new proof of Ito's theorem2000In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 28, p. 5353-5362Article in journal (Refereed)
  • 17.
    Tveiten, Ketil
    Stockholm University, Faculty of Science, Department of Mathematics.
    B-splines, polytopes and their characteristic D-modulesIn: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125Article in journal (Refereed)
    Abstract [en]

    Given a polytope σ⊂R m  , its characteristic distribution δ σ   generates a D -module which we call the characteristic D -module of σ  and denote by M σ  . More generally, the characteristic distributions of a cell complex K  with polyhedral cells generate a D -module M K  , which we call the characteristic D -module of the cell complex. We prove various basic properties of M K  , and show that under certain mild topological conditions on K , the D -module theoretic direct image of M K   coincides with the module generated by the B -splines associated to the cells of K  (considered as distributions). We also give techniques for computing D -annihilator ideals of polytopes.

  • 18.
    Xantcha, Qimh Richey
    Stockholm University, Faculty of Science, Department of Mathematics.
    Polynomial Maps of Modules2017In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, no 9, p. 4109-4122Article in journal (Refereed)
    Abstract [en]

    The article focuses on three different notions of polynomiality for maps of modules. In addition to the polynomial maps studied by Eilenberg and Mac Lane and the strict polynomial maps (“lois polynomes”) considered by Roby, we introduce numerical maps and investigate their properties. Even though our notion requires the existence of binomial coefficients in the base ring, we argue that it constitutes the correct way to extend Eilenberg and Mac Lane’s polynomial maps of abelian groups to incorporate modules over more general rings. The main theorem propounds that our maps admit a description corresponding, word by word, to Roby’s definition of strict polynomial maps.

1 - 18 of 18
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