关于环自同态的相对McCoy性质
ON RELATIVE MCCOY PROPERTIES WITH A RING ENDOMORPHISM

本文引入了α-McCoy环和弱α-McCoy环的概念分别研究了一个环R关于其自同态α的McCoy性质和弱McCoy性质. 利用各种环扩张, 证明了一个环R是α-McCoy环当且仅当R[x]是α-McCoy环, 得到了正向系上弱α-McCoy 环的正向极限是弱α-McCoy环, 推广和改进了McCoy环在矩阵环和多项式上的相关结论.
In this paper, we introduce the notions of an α-McCoy ring and weak α-McCoy rings to study McCoy properties and weak McCoy properties relative to an endomorphism α of a ring R. By using various ring extensions, we prove that a ring R is a right α-McCoy ring if and only if R[x] is a right α-McCoy ring, and the direct limit of a direct system of right weak α-McCoy rings is investigated in the last section. It is shown that if R is a right weak α-McCoy ring. Some well-known results on McCoy rings are generalized