Maximal Ideal Theorem and the Axiom of Choice

22 June 2017
June 22, 2017
Contatti: 
Staff Dipartimento di Matematica

Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it

Luogo: Seminar Room “-1” – Department of Mathematics - Via Sommarive 14 - Povo -Trento
at 14:00 a.m.

  • Augustine Musukwa - PhD in mathematics

Abstract:
In Zermelo-Fraenkel Set Theory with Choice (ZFC), there are several axioms that formulate a theory of sets and Axiom of Choice (AC) is one of them. Though it is crucial in most modern mathematics, Axiom of Choice has generated the most controversy. It has to be mentioned explicitly whenever used outside of set theory, while the use of the other axioms often goes unmentioned. In literature, there have been many attempts to show statements which are equivalent to AC. In this talk, we show that AC and the stamement: “every unique factorization domain has a maximal ideal” are equivalent. We employ approaches by Krull and Banaschewski.

Key words: Axiom of Choice, maximal ideal, spread, Zorn’s lemma

Scientific Coordinator: Stefano Baratella