The probability that ideals in a number ring are k-wise relatively r-prime-Reference-Cited by-同舟云学术

The probability that ideals in a number ring are k-wise relatively r-prime

Published:2020-07-02 Issue:08 Volume:16 Page:1753-1765
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Sittinger Brian D.¹^ORCID,DeMoss Ryan D.²

Affiliation:

1. Department of Mathematics, CSU Channel Islands, 1 University Drive, Camarillo, California 93012, USA

2. Department of Mathematics, California Lutheran University, 60 West Olsen Road, Thousand Oaks, California 91360, USA

Abstract

We say that [Formula: see text] nonzero ideals of algebraic integers in a fixed number ring are [Formula: see text]-wise relatively [Formula: see text]-prime if any [Formula: see text] of them are relatively [Formula: see text]-prime. In this paper, we provide an exact formula for the probability that [Formula: see text] nonzero ideals of algebraic integers in a fixed number ring are [Formula: see text]-wise relatively [Formula: see text]-prime.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500918

Reference8 articles.

1. The probability that k positive integers are relatively r-prime

2. THE PROBABILITY THAT RANDOM POSITIVE INTEGERS ARE k-WISE RELATIVELY PRIME

3. On the probability that k positive integers are relatively prime

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