# Reverse Mathematics of Divisibility in Integral Domains

Version 2 2022-03-21, 02:01

Version 1 2021-11-13, 03:29

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

2013-01-01## Date of Award

2013-01-01## Publisher

Te Herenga Waka—Victoria University of Wellington## Rights License

Author Retains Copyright## Degree Discipline

Mathematics## Degree Grantor

Te Herenga Waka—Victoria University of Wellington## Degree Level

Masters## Degree Name

Master of Science## Victoria University of Wellington Item Type

Awarded Research Masters Thesis## Language

en_NZ## Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research## Advisors

Greenberg, Noam## Usage 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

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