• Algebras of Finite Representation Type 

      Oldervoll, Marte (Master thesis, 2014)
      In this thesis we are considering finite dimensional algebras. We prove that any basic and indecomposable finite dimensional algebra A over an algebraically closed field k is isomorphic to a bound quiver algebra. Furthermore, ...
    • Classifying Subcategories in Quotients of Exact Categories - Classifying Triangulated and Thick Triangulated Subcategories of an Algebraic Triangulated Category 

      Arentz-Hansen, Emilie B (Master thesis, 2017)
      The goal of this thesis is to prove a one-to-one correspondence between (thick) triangulated subcategories of the stable category associated with a Frobenius category and certain subcategories of the Frobenius category. ...
    • Classifying Subcategories of Triangulated Categories 

      Haugland, Johanne (Master thesis, 2018)
      The topic of this thesis is classification of subcategories of triangulated categories. We first state and prove the Hopkins-Neeman theorem, which gives a bijection between thick subcategories of the derived category of ...
    • Classifying Tensor Triangulated Subcategories 

      Eggen, Magnus (Master thesis, 2018)
      We define triangulated and tensor triangulated categories, and classify the thick subcategories of a specific tensor triangulated category using Paul Balmer s theory on the categorical spectrum.
    • Gröbner-baser og signaturskjemaet Unbalanced Oil and Vinegar 

      Kvåle, Jarle (Master thesis, 2009)
      Vi har i denne masteroppgaven sett nærmere på Gröbner-baser og signaturskjemaet Unbalanced Oil and Vinegar. Vi har sett nærmere på Gröbner-basenes definisjoner og sett hvordan Gröbner-baser kan genereres ved Buchbergers ...
    • Gröbnerbaser og kryptosystemet HFE 

      Kolden, Jon Inge (Master thesis, 2009)
      I denne masteroppgaven ser vi nærmere på Gröbner-baser og kryptosystemet Hidden Field Equations. Vi begynner med å se på flere algebraiske begreper knyttet til Gröbner-baser, og hvordan Gröbner-baser kan beregnes vha. ...
    • Hochschild cohomology, complexity and support varieties 

      Bergh, Petter Andreas (Doktoravhandlinger ved NTNU, 1503-8181; 2006:234, Doctoral thesis, 2006)
      This PhD-thesis consists of the five papers - On the Hochschild (co)homology of quantum exterior algebras, to appear in Comm. Algebra, -Complexity and periodicity, Coll. Math. 104 (2006), no. 2, 169-191, -Twisted support ...
    • Hochschild homology and trivial extension algebras 

      Bergh, Petter Andreas; Madsen, Dag Oskar (Journal article; Peer reviewed, 2017)
      We prove that if an algebra is either selfinjective, local or graded, then the Hochschild homology dimension of its trivial extension is infinite.
    • Idealfaktorisering i Dedekindområder 

      Øyen, Kristine Tynes (Master thesis, 2013)
      Vi har studert forskjellige klasser av integritetsområder og sett på noen egenskaper hos disse.Vi har definert et Dedekindområde og vist at ethvert ekte ikke-null ideal i et slikt område kan faktoriseres unikt til et produkt ...
    • Integral Group Cohomology 

      Sveinsson, Gunnar Arvid (Master thesis, 2017)
      In this thesis we look closer at properties of integral group cohomology. In particular, we introduce the Lyndon-Hochschild-Serre spectral sequence which has a useful product structure which we use to prove that the group ...
    • Matrix factorizations for quantum complete intersections 

      Bergh, Petter Andreas; Erdmann, Karin (Peer reviewed; Journal article, 2019)
      We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective ...
    • Matrix factorizations for self-orthogonal categories of modules 

      Bergh, Petter Andreas; Thompson, Peder (Peer reviewed; Journal article, 2020)
      For a commutative ring S and self-orthogonal subcategory C of Mod(S), we consider matrix factorizations whose modules belong to C. Let f∈S be a regular element. If f is M-regular for every M∈C, we show there is a natural ...
    • On support varieties and tensor products for finite dimensional algebras 

      Bergh, Petter Andreas; Sandøy, Mads Hustad; Solberg, Øyvind (Peer reviewed; Journal article, 2020)
      It has been asked whether there is a version of the tensor product property for support varieties over finite dimensional algebras defined in terms of Hochschild cohomology. We show that in general no such version can ...
    • Realizability and the Avrunin-Scott theorem for higher-order support varieties 

      Bergh, Petter Andreas; Jorgensen, David Alan (Journal article; Peer reviewed, 2018)
      We introduce higher-order support varieties for pairs of modules over a commutative local complete intersection ring and give a complete description of which varieties occur as such support varieties. In the context of a ...
    • Serre's Conjecture: Finitely generated projective modules over polynomial rings 

      Sandbakk, Fredrik (Master thesis, 2013)
      We start by proving that all finitely generated projective R-modules, where R=k[x(1),...,x(n)] and k is a field, are stably free. Then we show that all stably free projective modules over a ring with the unimodular column ...
    • Subcategory Classifications in Tensor Triangulated Categories 

      Sigstad, Henrik (Master thesis, 2011)
      It is known that the thick tensor-ideal subcategories in a tensor triangulated cate-gory can be classified via its prime ideal spectrum.We use this to provide new proofs of two well-known classifications theorems:that of ...
    • The Fundamental Group of SO(3) 

      Mork, Eirik Andreas (Master thesis, 2014)
      We study fundamental groups of topological spaces. In particular we will compute the fundamental group of SO(3), the group of rotations in three dimensions, by studying covering spaces. We will see that the fundamental ...
    • The Homotopy Theory of (∞,1)-Categories 

      Hellstrøm-Finnsen, Magnus (Master thesis, 2014)
      The homotopy category of a stable (∞,1)-category can be endowed with a triangulated structure. The main objective of this thesis is to give a proof of this fact. First it will be discussed some ideas of higher category ...
    • Triangulated Categories and Matrix Factorizations 

      Langfeldt, Marit Buset (Master thesis, 2016)
      In this thesis we study triangulated categories and look at one specific example, the homotopy category of matrix factorizations. First we define categories and functors. Then we introduce additive and triangulated categories ...
    • Unique factorization in Dedekind domains 

      Engdal, Simen Einmo (Master thesis, 2016)
      In this thesis we study ideals in Dedekind domains, which factorize uniquely into a product of prime ideals. As not every Dedekind domain is a unique factorization domain, a general element in these domains does not ...