广西师范学院学报(自然科学版)
廣西師範學院學報(自然科學版)
엄서사범학원학보(자연과학판)
JOURNAL OF GUANGXI TEACHERS EDUCATION UNIVERSITY(NATURAL SCIENCE EDITION)
2009年
1期
1-10
,共10页
四元数代数%极大理想%极大单边理想%素谱%Jacobson根
四元數代數%極大理想%極大單邊理想%素譜%Jacobson根
사원수대수%겁대이상%겁대단변이상%소보%Jacobson근
quaternion algebra%maximal ideal%maximal one-sided ideal%prime spectrum%Jacobson radical
Z n 上的四元数环Z n [i,j,k]是一个Z n 上的代数.该文研究Z n [i,j,k]的相关性质并证明Z n [i,j,k]是一个局部环当且仅当n为2的方幂.并且,完全确定了Z n [i,j,k]的极大单边理想,极大双边理想,素谱和Jacobson根.
Z n 上的四元數環Z n [i,j,k]是一箇Z n 上的代數.該文研究Z n [i,j,k]的相關性質併證明Z n [i,j,k]是一箇跼部環噹且僅噹n為2的方冪.併且,完全確定瞭Z n [i,j,k]的極大單邊理想,極大雙邊理想,素譜和Jacobson根.
Z n 상적사원수배Z n [i,j,k]시일개Z n 상적대수.해문연구Z n [i,j,k]적상관성질병증명Z n [i,j,k]시일개국부배당차부당n위2적방멱.병차,완전학정료Z n [i,j,k]적겁대단변이상,겁대쌍변이상,소보화Jacobson근.
The ring of quaternions over Z n which is denoted by Z n [i, j, k] is a quaternion algebra. In this paper, we investigate the properties of Z n [i, j, k] and it is shown that Z n [i, j, k] is a local ring if and only if n=2t with t≥1. We completely determine the maximal one-sided ideals, maximal two-sided ideals, the prime spectrum and the Jacobson radical of Z n [i, j, k].