Blar i Institutt for matematiske fag på emneord "Algebra"

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    • An Analysis of a Cryptographic Communication Protocol 

      Strand, Maria (Master thesis, 2010)
      We have considered a cryptographic communication protocol and given a proof for its security.

    • Auslander-Reiten components containing modules of finite complexity 

      Toft, Tea (Master thesis, 2011)
      Let R be a connected selfinjective Artin algebra. We prove that any almost split sequence ending at an Omega-perfect R-module of finite complexity has at most four non-projective summands in a chosen decomposition of the ...

    • Cluster categories and cluster-tilted algebras 

      Torkildsen, Hermund Andre (Master thesis, 2006)
      We have given an introduction to the theory of cluster categories and cluster-tilted algebras, and this was one of our main objectives in this thesis. We have seen that cluster-tilted algebras are relation-extension algebras, ...

    • Connectednes of the Cluster Complex 

      Grimeland, Benedikte (Master thesis, 2009)
      The cluster complex of a basic hereditary artin algebra is defined, by constructing a poset T_H. A proof is given that the poset T_H is an abstract simplicial polytope. We define tilting modules, the Bongartz complement, ...

    • Connectedness of the Tilting Graph 

      Grimeland, Yvonne (Master thesis, 2009)
      We show that for a basic hereditary artin algebra over a commutative artin ring, the poset called the cluster complex of the algebra has the structure of an abstract simplicial polytope. From this result one can deduce ...

    • Counting Points on Elliptic Curves 

      Birkedal, Ole Andre Blom (Master thesis, 2010)
      In this paper we present the first efficient point counting algorithm due to Schoof, before giving a significant improvement due to Elkies. In the final section I give Satoh's algorithm which is even faster and has paved ...

    • Degeneration as a Partial Order on Module Categories 

      Ellingsen, Steinar (Master thesis, 2007)
      Chapter 1 contains most of the background material for this thesis. In Chapter 2 we provide a formal method for determining degeneration for algebras of finite representation type. In Chapter 3 we give an alternative ...

    • Elementary algebra as a modelling tool: A plea for a new curriculum 

      Strømskag, Heidi; Chevallard, Yves (Peer reviewed; Journal article, 2022)
      Elementary algebra is the foundation on which the entire modern mathematical edifice rises. But the algebraic curriculum fashioned by the process of didactic transposition for more than a century is no longer able to ensure ...

    • Finding Points on Elliptic Curves Modulo Composites 

      Karlsen, Jon Auklend (Master thesis, 2010)
      We consider the problem of finding points on elliptic curves over the ring of integers modulo an RSA modulus. Finding points on this curve seems to be hard, and we attack the problem from three different points of view.

    • Finding Small Roots of Polynomial Equations Using Lattice Basis Reduction 

      Sletta, Ingeborg (Master thesis, 2009)
      Using the LLL-algorithm to find small roots of polynomial equations using lattice basis reduction.

    • Gröbnerbasis: Algoritmer og kryptografi 

      Arnesen, Kristin Krogh (Master thesis, 2010)
      Del 1 er en innføring i kommutative og ikke-kommutative Gröbnerbasiser. Sentrale resultater og noen anvendelser. Del 2 handler om algoritmer. For kommutative Gröbnerbasiser ser vi på forbedringer av Buchbergers algoritme, ...

    • Improving the Norwegian Internet Voting Protocol 

      Øberg, Marianne Wiik (Master thesis, 2011)
      We have in this thesis looked at possible improvements with respect to security for the Norwegian Internet voting protocol. We have made a new protocol with independent secret keys, where all the encryptions of the votes ...

    • Koszul Algebras and Linear Modules: An introduction to the theory of Koszul algebras and linear modules. 

      Friis, Pernille (Master thesis, 2010)
      In this thesis Koszul algebras and their modules, so called linear modules, are introduced. In order to do so, graded $K$-algebras, where $K$ is a field, are also defined and discussed. Furthermore, an isomorphism between ...

    • Koszul-algebraer over endelige kropper 

      Sundtjønn, Trude Pedersen (Master thesis, 2008)
      Vi har i denne masteroppgaven sett på Koszul-algebraer. Vi har definert Koszul-algebraer som graderte algebraer hvor de simple modulene har en lineær gradert projektiv oppløsning, og vi har bevist forskjellige karakteriseringer ...

    • Koszul-algebraer over endelige kropper 

      Olsen, Kari-Lise Frisvold (Master thesis, 2008)
      Masteroppgaven er innen algebra, nærmere bestemt Koszul-teori for algebraer. Koszul-algebraer, ble først definert av Priddy, har en sentral rolle innen algebra, geometri og topologi. Projektive moduler er viktige for å ...

    • Partial Orders in Representation Theory of Algebras 

      Nornes, Nils Melvær (Master thesis, 2008)
      In this paper we investigate some partial orders used in representation theory of algebras. Let $K$ be a commutative ring, $Lambda$ a finitely generated $K$-algebra and $d$ a natural number. We then study partial orders ...

    • Quivers and admissible relations of tensor products and trivial extensions 

      Skartsæterhagen, Øystein Ingmar (Master thesis, 2011)
      We show how to find quotients of path algebras isomorphic to tensor products, triangular matrix algebras and trivial extensions.

    • Root Systems, Cluster Algebras and Triangulations of a Regular n-gon 

      Alne, Katrine (Master thesis, 2010)
      This thesis introduces the concepts of root systems, quivers, Dynkin diagrams, triangulation of polygons and cluster algebra. The main goal is to find a connection between all these topics.

    • The 4 Subspace Problem 

      Forbregd, Tore A. (Master thesis, 2008)
      We present a complete solution to the 4 subspace problem in the generality of an algebraically closed eld. We do this by means of Auslander-Reiten theory and give the Auslander-Reiten quiver of the extended $D_4$ Dynkin ...

    • The Ungraded Derived Category 

      Stai, Torkil Utvik (Master thesis, 2012)
      By means of the ungraded derived category we prove that the orbit category of the bounded derived category of an iterated tilted algebra with respect to translation is triangulated in such a way that the canonical functor ...