Search for dissertations about: "Homological algebra"

Showing result 1 - 5 of 8 swedish dissertations containing the words Homological algebra.

  1. 1. N-complexes and Categorification

    Author : Djalal Mirmohades; Volodymyr Mazorchuk; Steffen Oppermann; Uppsala universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Homological algebra; Category theory; Triangulated categories; K-theory; Hopfological algebra; Mathematics; Matematik;

    Abstract : This thesis consists of three papers about N-complexes and their uses in categorification. N-complexes are generalizations of chain complexes having a differential d satisfying dN = 0 rather than d2 = 0. Categorification is the process of finding a higher category analog of a given mathematical structure. READ MORE

  2. 2. Constructions of n-cluster tilting subcategories using representation-directed algebras

    Author : Laertis Vaso; Martin Herschend; Øyvind Solberg; Uppsala universitet; []
    Keywords : NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Representation theory; n-cluster tilting subcategory; Auslander–Reiten theory; representation-directed algebra; Nakayama algebra; global dimension; Mathematics; Matematik;

    Abstract : One of the most useful tools in representation theory of algebras is Auslander–Reiten theory. A higher dimensional analogue has recently appeared, based on the notion of n-cluster tilting subcategories. READ MORE

  3. 3. Complexes and Diffrerential Graded Modules

    Author : Dmitri Apassov; Matematik (naturvetenskapliga fakulteten); []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; algebraic geometry; field theory; Number Theory; fiber of a local homomorphism; DG dualizing module; homological dimensions; differential graded rings; almost finite module; Cohen-Macaulay rings; local homomorphism; Gorenstein rings; annihilator; complex of modules; algebra; group theory; Talteori; fältteori; algebraisk geometri; gruppteori;

    Abstract : The main topic of the thesis is the generalization of some traditional module-theoretic homological applications to complexes of modules and to differential graded modules over differential graded rings. We introduce three possible generalizations of the classical notion of annihilator of an R-module. READ MORE

  4. 4. Applications of homological methods in commutative algebra

    Author : Gunnar Sjödin; []

    Abstract : .... READ MORE

  5. 5. Formalizing Refinements and Constructive Algebra in Type Theory

    Author : Anders Mörtberg; Göteborgs universitet; Göteborgs universitet; Gothenburg University; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Formalization of mathematics; refinements; constructive algebra; type theory; Coq; SSReflect;

    Abstract : The extensive use of computers in mathematics and engineering has led to an increased demand for reliability in the implementation of algorithms in computer algebra systems. One way to increase the reliability is to formally verify that the implementations satisfy the mathematical theorems stating their specification. READ MORE