四元数环与四元数函子

QUATERNION RINGS AND QUATERNION FUNCTORS

本文给出了交换环上的四元数环是除环的两个充要条件；在环范畴的子范畴间定义了四元数函子，并证明了它是一个正合函子，同时讨论了环类的遗传性，同态闭性在四元数函子下的变化情况．

In this paper, some characterizations of rings R for which the quaternion ring Q(R) is a diuision ring have been given. We defined the quaternion functor Q on rings categories,and proved that Q is an exact functor.