中文摘要：

证明了环理论扩充到具有量词消去理论时，其任意模型都是归纳环，而且带有一阶可定义序关系的环理论扩充到具有量词消去时，其模型是双向归纳环．

英文摘要：

It is shown that if ring theory is added to a new theory which has quantifier elimination, any model of this new theory is an inductive ring. It is also shown that if ring theory with a first-order definable order relation is added to a new theory which has quantifier elimination, any model of this new theory is a hi- inductive ring.