Sökning: "Commutative algebra"
Visar resultat 1 - 5 av 49 avhandlingar innehållade orden Commutative algebra.
1. Waring-type problems for polynomials : Algebra meets Geometry
Sammanfattning : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. LÄS MER
2. Centra of Quiver Algebras
Sammanfattning : A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. LÄS MER
3. Bounds on Hilbert Functions
Sammanfattning : This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectorsof reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. LÄS MER
4. On a class of commutative algebras associated to graphs
Sammanfattning : In 2004 Alexander Postnikov and Boris Shapiro introduced a class of commutative algebras for non-directed graphs. There are two main types of such algebras, algebras of the first type count spanning trees and algebras of the second type count spanning forests. LÄS MER
5. Amenable-like properties of étale groupoids
Sammanfattning : This thesis consists of three papers related to analytic and representation theoretic properties of étale groupoids.In the first paper, we characterize algebraically the type I and CCR property for ample groupoids and their non-commutative duals: Boolean inverse semigroups. Our results use and generalize Thoma’s work on discrete groups. LÄS MER