一类环上HX环的结构

The Structure of HX Ring on A Class of Ring

自李洪兴１９９１年提出了ＨＸ环以来，人们一直有这么一个问题没解决，就是是否存在非平凡的ＨＸ环的例子？但至今既没找到非平凡的ＨＸ环，也没有证明任一环Ｒ仅存在平凡的ＨＸ环。针对这个问题，本文提出并证明了一类环仅有平凡ＨＸ环，还给出了一系列的结构定理。这样，既为证明任一环Ｒ仅有平凡的ＨＸ环的猜想有新的启示，也为人们指明无须在这一类环上寻找非平凡ＨＸ环。

since the HX ring was raked by prof. Li Hong Xing in 1991,the problem of non-trivial HX ring existing has been unsolved. However,we find neithernon-trivial HX ring nor any ring only existing trivial HX ring, As for this,this paper point out that a class of ring exist trivial HX ring only and give a serious of structure theorems. Espec-tially, we may have some new ideas on either proving the existing trivial HX ring hy-pothesis of any ring or pointing out the course of forming non-trivial HX ring.