强symmetric环

Strongly Symmetric Rings

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.