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  • 1.
    Källström, Rolf
    et al.
    Department of Mathematics, University of Gävle, Sweden.
    Tadesse, Yohannes
    Department of Mathematics, University of Stockholm, Sweden.
    Hilbert series of modules over Lie algebroids2015In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 432, p. 129-184Article in journal (Refereed)
    Abstract [en]

    We consider modules M over Lie algebroids gA which are of finite type over a local noetherian ring A. Using ideals J ⊂ A such that gA ·J ⊂ J and the length ℓgA (M/JM) < ∞ we can define in a natural way the Hilbert series of M with respect to the defining ideal J. This notion is in particular studied for modules over the Lie algebroid of k-linear derivations gA = TA(I) that preserve an ideal I ⊂ A, for example when A = On, the ring of convergent power series. Hilbert series over Stanley-Reisner rings are also considered.

  • 2.
    Sjögren, Jörgen
    University of Skövde, School of Life Sciences. Department of Philosophy/Logic, University of Göteborg, Gothenburg, Sweden.
    On explicating the concept the power of an arithmetical theory2008In: Journal of Philosophical Logic, ISSN 0022-3611, E-ISSN 1573-0433, Vol. 37, no 2, p. 183-202Article in journal (Refereed)
    Abstract [en]

    In this paper I discuss possible ways of measuring the power of arithmetical theories, and the possiblity of making an explication in Carnap’s sense of this concept. Chaitin formulates several suggestions how to construct measures, and these suggestions are reviewed together with some new and old critical arguments. I also briefly review a measure I have designed together with some shortcomings of this measure. The conclusion of the paper is that it is not possible to formulate an explication of the concept.

  • 3.
    Tadesse, Yohannes
    Department of Mathematics, Addis Ababa University, Ethiopia ; Department of Mathematics, Stockholm University, Sweden.
    Derivations Preserving a Monomial Ideal2009In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 137, no 9, p. 2935-2942Article in journal (Refereed)
    Abstract [en]

    Let I be a monomial ideal in a polynomial ring A = k[x1, . . . ,xn] over a field k of characteristic 0, TA/k(I) be the module of I-preserving k-derivations on A and G be the n-dimensional algebraic torus on k. We computethe weight spaces of TA/k(I) considered as a representation of G. Using this, we show that TA/k(I) preserves the integral closure of I and the multiplierideals of I.

  • 4.
    Tadesse, Yohannes
    Department of Mathematics, Stockholm University, Sweden.
    Poincaré Series of Monomial Rings with Minimal Taylor Resolution2011Manuscript (preprint) (Other academic)
    Abstract [en]

    We give a comparison between the Poincare series of two monomial rings: R=A/I and Rq=A/Iq where Iq is a monomial ideal generated by the q'th power of monomial generators of I. We compute the Poincare series for a class of monomial rings with minimal Taylor resolution. The paper was produced during Pragmatic 2011. 

  • 5.
    Tadesse, Yohannes
    Department of Mathematics, Stockholm University, Sweden.
    Poincaré series of monomial rings with minimal Taylor resolution2012In: Le Matematiche, ISSN 0373-3505, Vol. 67, no 1, p. 119-128Article in journal (Refereed)
    Abstract [en]

    We give a comparison between the Poincaré series of two monomial rings: R = A/I and R_q = A/I_q where I_q is a monomial ideal generated by the q’th power of monomial generators of I. We compute the Poincaré series for a new class of monomial ideals with minimal Taylor resolution. We also discuss the structure a monomial ring with minimal Taylor resolution where the ideal is generated by quadratic monomials.

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  • 6.
    Tadesse, Yohannes
    Stockholms universitet, Matematiska institutionen.
    Tangential Derivations, Hilbert Series and Modules over Lie Algebroids2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Let A/k be a local commutative algebra over a field k of characteristic 0, and T_{A/k} be the module of k-linear derivations on A. We study, in two papers, the set of k-linear derivations on A which are tangential to an ideal I of A (preserves I), defining an A-submodule T_{A/k}(I) of T_{A/k}, which moreover is a k-Lie subalgebra. More generally we consider Lie algebroids g_A over A and modules over g_A.

    Paper I: Using the action of an algebraic torus on a monomial ideal in a polynomial ring A=k[x_1,..., x_n] we:

    • give a new proof of a description of the set of tangential derivations T_{A/k}(I) along a monomial ideal I, first proven by Brumatti and Simis.
    • give a new and direct proof to the fact that the integral closure of a monomial ideal is monomial. We also prove that a derivation which is tangential to a monomial ideal will remain tangential to its integral closure.
    • prove that a derivation which is tangential to a monomial ideal is also tangential to any of its associated multiplier ideals.

    Paper II: We consider modules M over a Lie algebroid g_A which are of finite type over A. In particular, we study the Hilbert series of the associated graded module of such a module with respect to an ideal of definition.

    Our main results are:

    • Hilbert's finiteness theorem in invariant theory is shown to hold also for a noetherian graded g_A-algebra S and a noetherian (S, g_A)-graded module which are semisimple over g_A.
    • We define a class of local system g_A-modules and prove that the Hilbert series of such a graded module is rational.  We also define an ideal of definition for a g_A-module M and prove rationality of the Hilbert series of M with respect to such an ideal.
    • We introduce the notion of toral Lie algebroids over a regular noetherian local algebra R and give some properties of modules over such Lie algebroids. In particular, we compute the Hilbert series of submodules of R over a Lie algebroid containig a toral Lie algebroid.
  • 7.
    Tadesse, Yohannes
    Department of Mathematics, Stockholm University, Sweden.
    The module of derivations preserving a monomial ideal2007Licentiate thesis, monograph (Other academic)
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