科研之友
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摘要
We introduce the concept of nil-McCoy rings to study the structure of the set of nilpotent elements in McCoy rings. This notion extends the concepts of McCoy rings and nil-Armendariz rings. It is proved that every semicommutative ring is nil-McCoy. We shall give an example to show that nil-McCoy rings need not be semicommutative. Moreover, we show that nil-McCoy rings need not be right linearly McCoy. More examples of nil-McCoy rings are given by various extensions. On the other hand, the properties of alpha-McCoy rings by considering the polynomials in the skew polynomial ring R[x; alpha] in place of the ring R[x] are also investigated. For a monomorphism alpha of a ring R, it is shown that if R is weak alpha-rigid and alpha-reversible then R is alpha-McCoy.
