HOW FAR IS AN ELEMENT FROM BEING PRIME?

Author:

ANDERSON DAVID F.1,CHAPMAN SCOTT T.2

Affiliation:

1. University of Tennessee, Department of Mathematics, Knoxville, TN 37996-1300, USA

2. Sam Houston University, Department of Mathematics and Statistics, Box 2206, Huntsville, TX 77341-2206, USA

Abstract

Let D be an integral domain. We investigate two invariants ω(D, x) and ω(D) which measure how far an x ∈ D is from being prime and how far an atomic integral domain D is from being a UFD, respectively. We give a new characterization of number fields with class number two. We also study asymptotic versions of these two invariants.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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1. The Importance of Being Prime , a Nontrivial Generalization for Nonunique Factorizations;The American Mathematical Monthly;2023-09-28

2. Asymptotic ω-Primality of Finitely Generated Cancelative Commutative Monoids;Mathematics;2023-02-04

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4. An improved algorithm to compute the $$\omega $$-primality;Optimization Letters;2020-05-21

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