唯一分解整环R上的多项式环R[x]  

Polynomial ring R[x]of unique factorization domain R

作　　者：卢梦霞[1] 凡美金 赵廷芳[1] 

机构地区：[1]周口师范学院数学与统计学院,河南周口466001

出　　处：《周口师范学院学报》2016年第5期55-56,共2页Journal of Zhoukou Normal University

基　　金：周口师范学院教学改革项目(No.J201215)

摘　　要：主要从三个方面来讨论唯一分解整环R上的多项式环R[x].首先,讨论了唯一分解整环R和R[x]的内在联系;其次,讨论了Q[x]中的元素f(x)的可约性;最后,讨论了R[x]中的元素f(x)的根和f(x)表达式中系数的关系.The properties of the polynomial ring R [x] of the ring R have been described in detail in many textbooks and papers. This paper mainly discusses the polynomial ring R [x ] of the unique factorization domain R from three aspects. First, the paper discusses the inner link between unique factorization domain R and R [x ] .Secondly, the paper discusses the reduc- ibility of element f（x ） in Q[x] .Finally, the paper discusses the relationship between the roots of element f（x） in Q[x] and the coefficients of f（x） expression.

关 键 词：唯一分解整环 商域 本原多项式 单位 

分 类 号：O153.3[理学—数学]