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  • 1. Atikaw, Sebsibew
    et al.
    Abebaw, Tilahun
    Bøgvad, Rikard
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On Bernstein-Sato ideals for central line arrangements2021Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 49, nr 10, s. 4123-4132Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The polynomial alpha=xy Pi(m)(i=3)(a(i)x+y)is an element of C[x,y] determines a plane central line arrangement alpha = 0. We compute explicitly multivariate Bernstein-Sato ideals of alpha by using the decomposition behavior of the D-2-module M-alpha(beta)=C[x,y,1/alpha]alpha(beta) given in earlier work by the authors. Our results are partially special cases of recent work in much greater generality, by Maisonobe on free hyperplane arrangements and Budur et al.) as well as Bath; however our proof is independent and gives some more information on different variants of Bernstein-Sato ideals in the simple plane case.

  • 2.
    Bøgvad, Rikard
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Gonçalves, Iara
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Decomposition of perverse sheaves on plane line arrangements2018Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 46, nr 6, s. 2476-2487Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 3. Carlini, Enrico
    et al.
    Oneto, Alessandro
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Polytechnic University of Turin, Italy.
    Monomials as Sums of k-th Powers of Forms2015Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 2, s. 650-658Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 4.
    Emtander, Eric
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Betti numbers of hypergraphs2009Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 37, nr 5, s. 1545-1571Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 5.
    Fröberg, Ralf
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Solution to a conjecture on edge rings with 2-linear resolutions2023Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 51, nr 4, s. 1447-1450Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    For a graph G=(V,E) the edge ring k[G] is k[x1,…,xn]/I(G), where n=|V| and I(G) is generated by {xixj;{i,j}∈E}. The conjecture we treat is the following.

    Conjecture 1. If k[G] has a 2-linear resolution, then the projective dimension of K[G], pd (k[G]), equals the maximal degree of a vertex in G.

    As far as we know, this conjecture is first mentioned in a paper by Gitler and Valencia, and there it is called the Eliahou-Villarreal conjecture. The conjecture is treated in a recent paper by Ahmed, Mafi, and Namiq. That there are counterexamples was noted already by Moradi and Kiani. By interpreting k[G] as a Stanley-Reisner ring, we are able to characterize those graphs for which the conjecture holds.

  • 6.
    Fröberg, Ralf
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Some comments to a result by Moreno2021Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 49, nr 6, s. 2704-2706Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Moreno studies the following question. Let I be an ideal in k[x1,…,xn] 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.

  • 7.
    Fröberg, Ralf
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Nicklasson, Lisa
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Università degli Studi di Genova, Italy.
    Gorenstein rings generated by strongly stable sets of quadratic monomials2022Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 50, nr 5, s. 2072-2082Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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 to a question by Migliore and Nagel. 

  • 8.
    Gottlieb, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    A proof that commutative Artinian rings are Noetherian1995Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, nr 12, s. 4687-4691Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 9.
    Gottlieb, Christian
    Stockholms universitet.
    An integer-valued function related to the number of generators of modules over local rings of small dimension1993Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 21, nr 11, s. 4115-4118Artikkel i tidsskrift (Fagfellevurdert)
  • 10.
    Gottlieb, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Bounding the number of generators for a class of ideals in local rings1995Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 23, nr 4, s. 1499-1502Artikkel i tidsskrift (Fagfellevurdert)
    Fulltekst (pdf)
    fulltext
  • 11.
    Gottlieb, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Finite unions of submodules2015Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 2, s. 847-855Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    Finite unions of submodules
  • 12.
    Gottlieb, Christian
    Stockholms universitet.
    Length and dimension modulo a Serre category1997Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 25, nr 5, s. 1553-1561Artikkel i tidsskrift (Fagfellevurdert)
  • 13.
    Gottlieb, Christian
    Stockholms universitet.
    Modules covered by finite unions of submodules1998Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 26, nr 7, s. 2351-2359Artikkel i tidsskrift (Fagfellevurdert)
  • 14.
    Gottlieb, Christian
    Stockholms universitet.
    On finite unions of ideals and cosets1994Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 22, nr 8, s. 3087-3097Artikkel i tidsskrift (Fagfellevurdert)
  • 15.
    Gottlieb, Christian
    Stockholms universitet.
    On generators of ideals in one-dimensional local rings1993Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 21, nr 2, s. 421-425Artikkel i tidsskrift (Fagfellevurdert)
  • 16.
    Gottlieb, Christian
    Stockholms universitet.
    On ideals which are almost zero, and related concepts1996Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 24, nr 6, s. 2201-2209Artikkel i tidsskrift (Fagfellevurdert)
  • 17.
    Gottlieb, Christian
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    The Nakayama Property of a Module and Related Concepts2015Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 12, s. 5131-5140Artikkel i tidsskrift (Fagfellevurdert)
    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. 

  • 18.
    Löfwall, Clas
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    DECOMPOSITION THEOREMS FOR A GENERALIZATION OF THE HOLONOMY LIE ALGEBRA OF AN ARRANGEMENT2016Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 44, nr 11, s. 4654-4663Artikkel i tidsskrift (Fagfellevurdert)
    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.

  • 19. Ma, Linquan
    et al.
    Pham, Hung
    Smirnov, Ilya
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Colength, multiplicity, and ideal closure operations2020Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 48, nr 4, s. 1601-1607Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then R is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.

  • 20.
    Nicklasson, Lisa
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    On the Hilbert series of ideals generated by generic forms2017Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, nr 8, s. 3390-3395Artikkel i tidsskrift (Fagfellevurdert)
    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.

    Fulltekst (pdf)
    fulltext
  • 21.
    Tambour, Torbjörn
    Stockholms universitet.
    The number of solutions of some equations in finite groups and a new proof of Ito's theorem2000Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 28, s. 5353-5362Artikkel i tidsskrift (Fagfellevurdert)
  • 22.
    Tveiten, Ketil
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    B-splines, polytopes and their characteristic D-modules2015Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 7, s. 2887-2902Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Given a polytope σ ⊂ ℝ m , its characteristic distribution δσ 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 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.

  • 23.
    Xantcha, Qimh Richey
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Polynomial Maps of Modules2017Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, nr 9, s. 4109-4122Artikkel i tidsskrift (Fagfellevurdert)
    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.

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