强symmetric环  

Strongly Symmetric Rings

作　　者：任艳丽[1] 徐之晓[1,2] 

机构地区：[1]南京晓庄学院数学系与信息技术学院,江苏南京210017 [2]辽宁师范大学数学学院,辽宁大连116029

出　　处：《数学的实践与认识》2010年第19期225-230,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471055);辽宁省教育厅科研基金(05L014)

摘　　要：为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x^(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环.Symmetric rings were introduced by lamber to unifg sheef representations of commutative rings and reduced rings.In this paper,we continue the study of symmetric rings,introduce the concept of strongly symmetric rings and investigate some properties of extensions.We proved that a ring R is a strongly symmetric ring if and only if R[x]isa strongly symmetric ring if and only if R[x;x^（-1）]is a strongly symmetric ring.We also proved that for a right Ore ring R with Q its classical right quotient ring,R is a strongly symmetric ring if and only if Q is a strongly symmetric ring.

关 键 词：symmetric环 强symmetric环 多项式环 经典商环 

分 类 号：O153.3[理学—数学]