Search for dissertations about: "power series algebra"

Showing result 1 - 5 of 11 swedish dissertations containing the words power series algebra.

  2. 1. Waring-type problems for polynomials : Algebra meets Geometry

    Author : Alessandro Oneto; Boris Shapiro; Brian Harbourne; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; polynomials; Waring problems; Hilbert series; fat points; power ideals; secant varieties; Mathematics; matematik;

    Abstract : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. READ MORE

  4. 2. Around power ideals : From Fröberg's conjecture to zonotopal algebra

    Author : Gleb Nenashev; Boris Shapiro; Volkmar Welker; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Mathematics; matematik;

    Abstract : In this thesis we study power algebras, which are quotient of polynomial rings by power ideals. We will study Hilbert series of such ideals and their other properties. We consider two important special cases, namely, zonotopal ideals and generic ideals. Such ideals have a lot combinatorial properties. READ MORE

  5. 3. Around minimal Hilbert series problems for graded algebras

    Author : Lisa Nicklasson; Samuel Lundqvist; Christian Gottlieb; Uwe Nagel; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Graded algebras; Hilbert series; Lefschetz properties; Exterior algebra; Linear resolution; Mathematics; matematik;

    Abstract : The Hilbert series of a graded algebra is an invariant that encodes the dimension of the algebra's graded compontents. It can be seen as a tool for measuring the size of a graded algebra. This gives rise to the idea of algebras with a "minimal Hilbert series", among the algebras within a certain family. READ MORE

  6. 4. The Diamond Lemma for Power Series Algebras

    Author : Lars Hellström; Umeå universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; diamond lemma; power series algebra; Gröbner basis; embedding into skew fields; archimedean element in semigroup; q-deformed Heisenberg--Weyl algebra; polynomial degree; ring norm; Birkhoff orthogonality; filtered structure; Matematisk analys; Mathematical analysis; Analys; Mathematics; matematik;

    Abstract : The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. READ MORE

  7. 5. Constructive Newton–Puiseux Theorem, Sheaf Model of the Separable Closure and Dynamic Evaluation

    Author : Bassel Mannaa; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Newton–Puiseux; Algebraic curve; Sheaf model; Dynamic evaluation; Algebraic number; Grothendieck topos; Grothendieck topos;

    Abstract : Computing the Puiseux expansions of a plane algebraic curve defined by an affine equation over an algebraically closed field is a an important algorithm in algebraic geometry. This is the so-called Newton–Puiseux Theorem. The termination of this algorithm, however, is usually justified by non-constructive means. READ MORE