Power-serieswise McCoy Rings

In this paper, we introduce power-serieswise McCoy rings, which are a generalization of power-serieswise Armendariz rings, and investigate their properties. We show that a ring R is power-serieswise McCoy if and only if the ring consisting of n × n upper triangular matrices with equal diagonal entries over R is power-serieswise McCoy. We also prove that a direct product of rings is power-serieswise McCoy if and only if each of its factors is power-serieswise McCoy. Meanwhile we show that power-serieswise McCoy rings may be neither semi-commutative nor power-serieswise Armendariz.