The Ideal Form of the Skew Polynomial Ring Over Quaternion

Abstract

This research was carried out in order to develop theory about the skew polynomial ring over non-commutative ring. This study aimed to find the ideal form of the skew polynomial ring over the quaternion. The research method was the library study. In order to find the ideal form of the skew polynomial ring over the quaternion, the first thing to do was finding the endomorphism form in the quaternion ring, which was symbolized by , and eleven endomorphisms were obtained. The research results every ring had two ideals form. In general, the rings which had the identically ideal forms were categorized into three: three rings were identical, two rings were also identical, and the rest six rings had identical forms too.