arXiv subjects
Publications and source records attributed to Brian D. Sittinger.
We say that n ideals of algebraic integers in a fixed number ring are k-wise relatively r-prime if any k of them are relatively r-prime. In this article, we provide an exact formula for the probability that n nonzero ideals of algebraic integers in a fixed number ring are k-wise relatively r-prime.
It has been established on many occasions that the set of quotients of prime numbers is dense in the set of positive real numbers. More recently, it has been proved that the set of quotients of primes in the Gaussian integers is dense in the complex plane. In this article, we not only extend this result to any imaginary quadratic number ring, but also prove that the set of quotients of primes in any real quadratic number ring is dense in the set of real numbers. To conclude, we show how to extend these results to an arbitrary algebraic number ring.