对称环的扩张

摘要

We first consider properties and basic extensions of symmetric rings. We next argue about the symmetry of some kinds of polynomial rings, and show that if R is a reduced ring then R[x]/(xn) is a symmetric ring, where (xn) is the ideal generated by xn and n is a positive integer. Consequently, we prove that for a right Ore ring R with Q its classical right quotient ring, R is symmetric if and only if Q is symmetric.%本文首先考虑了对称环的性质和基本的扩张.其次讨论了几种多项式环的对称性,且证明了:如果R是约化环,则R[x]/(xn)是对称环,其中(xn)是由xn生成的理想,n是一个正整数.最后证明了:对一个右Ore环R,R是对称环当且仅当R的古典右商环Q是对称环.