循环环的商环的结构

On the Structure of the Quotient Ring of a Circular Ring

首先研究了一般循环环的商环,得到循环环的商环仍是循环环,并给出了其生成元.然后,在此基础上进一步研究了有限循环环和无限循环环的商环,并给出了它们的阶.

In this paper, the quotient ring of a general circular ring is studied, it is got that the quotient ringofageneral circularring is alsoa circularring, and its generator is given out. On the basis, then, the quotient rings of a finite cyclic ringand a infinite cyclic ring are further studied, and their ordersare givenout.