Ahimbisibwe, Godfrey2024-12-292024-12-292024Ahimbisibwe, Godfrey (2024). Factorisation Theory in Submonoids Of (ℕ, X). Kabale: Kabale University.http://hdl.handle.net/20.500.12493/2585This research investigates the factorization behavior in submonoids of (ℕ, x). In particular, it identifies and describes specific submonoids of (ℕ, X) that have non-unique factorizatios of elements. Furthermore, it investigates the sets of lengths of elements in certain submonoids of (ℕ, X). For instance, we have proved the existence of atoms (irreducibles) in Hilbert`s monoid and Meyerson`s monoid giving a basic description of their sets of lengths and how they differ based on their factorization into their atoms (irreducibles) in ℕ.enAttribution-NonCommercial-NoDerivs 3.0 United Stateshttp://creativecommons.org/licenses/by-nc-nd/3.0/us/Factorisation TheorySubmonoids(ℕX)Thesis