Sökning: "introduction to algebra"
Visar resultat 1 - 5 av 20 avhandlingar innehållade orden introduction to algebra.
1. Simple Modules over Lie Algebras
Sammanfattning : Simple modules are the elemental components in representation theory for Lie algebras, and numerous mathematicians have worked on their construction and classification over the last century. This thesis consists of an introduction together with four research articles on the subject of simple Lie algebra modules. LÄS MER
2. A Natural Interpretation of Classical Proofs
Sammanfattning : In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. LÄS MER
3. On properties of monomial ideals and algebras
Sammanfattning : Monomial ideals form an important link between commutative algebra and combinatorics. Our aim is to study various operations on monomial ideals and algebras, as well as their properties. This thesis consists of an introduction and four research articles. The introduction covers the necessary background and the existing results. LÄS MER
4. Configuration spaces, props and wheel-free deformation quantization
Sammanfattning : The main theme of this thesis is higher algebraic structures that come from operads and props.The first chapter is an introduction to the mathematical framework needed for the content of this thesis. The chapter does not contain any new results. LÄS MER
5. A Proof and Formalization of the Initiality Conjecture of Dependent Type Theory
Sammanfattning : In this licentiate thesis we present a proof of the initiality conjecture for Martin-Löf’s type theory with 0, 1, N, A+B, ∏AB, ∑AB, IdA(u,v), countable hierarchy of universes (Ui)iєN closed under these type constructors and with type of elements (ELi(a))iєN. We employ the categorical semantics of contextual categories. LÄS MER