Reverse Mathematics of Divisibility in Integral Domains
thesisposted on 2022-03-21, 02:01 authored by Bura, Valentin B
This 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.
Date of Award2013-01-01
PublisherTe Herenga Waka—Victoria University of Wellington
Rights LicenseAuthor Retains Copyright
Degree GrantorTe Herenga Waka—Victoria University of Wellington
Degree NameMaster of Science
Victoria University of Wellington Item TypeAwarded Research Masters Thesis
Victoria University of Wellington SchoolSchool of Mathematics, Statistics and Operations Research
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 Science