The ideals of the hurwitzean polynomial ring

1 February 1976

journal article
research article
Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society

Vol. 14 (1) , 37-61
https://doi.org/10.1017/s0004972700024849

Abstract

In 1919, Adolf Hurwitz formed the quaternion ring R composed of elements whose coordinates were either all integers or halves of odd integers. The objective of this paper is to examine the (two-sided) ideal structure in the hurwitzean polynomial ring R[x], formed by taking all polynomials with coefficients in R. The maximal and prime ideals of R[x] will be characterized with results surprisingly analogous to those in Z[x]. In addition, a canonical basis, of the type developed by G. Szekeres, 1952, for polynomial domains, will be developed for the ideals of R[x].

Keywords

This publication has 1 reference indexed in Scilit:

A Canonical Basis for the Ideals of a Polynomial Domain
The American Mathematical Monthly, 1952