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Showing result 1 - 5 of 105 swedish dissertations matching the above criteria.

  2. 1. Canonical Bases for Algebraic Computations

    Author : Patrik Nordbeck; Algebra; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; gruppteori; algebra; algebraisk geometri; fältteori; Talteori; group theory; algebraic geometry; field theory; Matematik; Number Theory; regular languages; Mathematics; composition of polynomials; factor algebras; Gröbner bases; SAGBI bases;

    Abstract : This thesis deals with computational methods in algebra, mainly focusing on the concept of Gröbner and SAGBI bases in non-commutative algebras. The material has a natural division into two parts. The first part is a rather extensive treatment of the basic theory of Gröbner bases and SAGBI bases in the non-commutative polynomial ring. READ MORE

  4. 2. Quaternion Orders and Ternary Quadratic Forms Orders of Class Number One and Representations of Algebraic Integers by Quadratic Forms

    Author : Elise Björkholdt; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; quaternion order; ternary quadratic form; class number; even Clifford algebra; quaternion algebra; embedding number; 11E12; 16H05; 11E20; 11E25; 11E88; even Clifford algebra;

    Abstract : Let R be the ring of integers in a totally real quadratic field K. The purpose of the thesis is to study totally definite quaternion R-orders and representations of elements in R by totally positive definite integral ternary quadratic forms. The thesis consists of three papers. READ MORE

  5. 3. 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

  6. 4. Quasi-Lie Algebras and Quasi-Deformations. Algebraic Structures Associated with Twisted Derivations

    Author : Daniel Larsson; Matematik LTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Talteori; fältteori; algebraisk geometri; algebra; gruppteori; Lie Algebras; Quasi-Deformations; Number Theory; field theory; algebraic geometry; group theory; Quasi-Lie Algebras;

    Abstract : This thesis introduces a new deformation scheme for Lie algebras, which we refer to as ?quasi-deformations? to clearly distinguish it from the classical Grothendieck-Schlessinger and Gers-tenhaber deformation schemes. The main difference is that quasi-deformations are not in gene-ral category-preserving, i.e. READ MORE

  7. 5. Ternary quadratic forms over algebraic integers

    Author : Elise Björkholdt; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; ternary quadratic form; quaternion order; even Clifford algebra; quaternation algebra; embedding number; quaternion order;

    Abstract : .... READ MORE