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# Reverse mathematics of rings

thesis

posted on 2021-10-19, 19:56 authored by Barrett, JordanUsing the tools of reverse mathematics in second-order arithmetic, as developed by Friedman, Simpson, and others, we determine the axioms necessary to develop various topics in commutative ring theory. Our main contributions to the field are as follows. We look at fundamental results concerning primary ideals and the radical of an ideal, concepts previously unstudied in reverse mathematics. Then we turn to a fine-grained analysis of four different definitions of Noetherian in the weak base system RCA_0 + Sigma-2 induction. Finally, we begin a systematic study of various types of integral domains: PIDs, UFDs and Bézout and GCD domains.

## History

## Copyright Date

2021-10-19## Date of Award

2021-10-19## Publisher

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

CC BY-NC-SA 4.0## Degree Discipline

Mathematics## Degree Grantor

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

Masters## Degree Name

Master of Science## ANZSRC Type Of Activity code

1 PURE BASIC RESEARCH## Victoria University of Wellington Item Type

Awarded Research Masters Thesis## Language

en_NZ## Victoria University of Wellington School

School of Mathematics and Statistics## Advisors

Turetsky, Dan## Usage metrics

## Keywords

reverse mathematicsNoetherian ringintegral domainSchool: School of Mathematics and Statistics010107 Mathematical Logic, Set Theory, Lattices and Universal AlgebraDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceMathematical Logic, Set Theory, Lattices and Universal Algebra

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