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

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.