Open Access Te Herenga Waka-Victoria University of Wellington
Browse
thesis_access.pdf (594.51 kB)

Reverse Mathematics of Divisibility in Integral Domains

Download (594.51 kB)
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 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.

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