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Download fileReverse Mathematics of Divisibility in Integral Domains
thesis
posted on 2022-03-21, 02:01 authored by Bura, Valentin BThis thesis establishes new results concerning the proof-theoretic
strength of two classic theorems of Ring Theory relating to
factorization in integral domains.
The first theorem asserts that if every irreducible is a prime, then
every element has at most one decomposition into irreducibles; the
second states that well-foundedness of divisibility implies the
existence of an irreducible factorization for each element.
After introductions to the Algebra framework used and Reverse Mathematics, we show that the first theorem is provable in the base system of Second Order Arithmetic RCA0, while the other is equivalent over RCA0 to the system ACA0.
History
Copyright Date
2013-01-01Date of Award
2013-01-01Publisher
Te Herenga Waka—Victoria University of WellingtonRights License
Author Retains CopyrightDegree Discipline
MathematicsDegree Grantor
Te Herenga Waka—Victoria University of WellingtonDegree Level
MastersDegree Name
Master of ScienceVictoria University of Wellington Item Type
Awarded Research Masters ThesisLanguage
en_NZVictoria University of Wellington School
School of Mathematics, Statistics and Operations ResearchAdvisors
Greenberg, NoamUsage metrics
Keywords
Reverse mathematicsCommutative algebraAlgebraSchool: School of Mathematics, Statistics and Operations Research010107 Mathematical Logic, Set Theory, Lattices and Universal AlgebraMarsden: 230101 Mathematical Logic, set Theory, Lattices and CombinatoricsMarsden: 230103 Rings and AlgebrasDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceMathematical Logic, Set Theory, Lattices and Universal Algebra