ON SKEW POWER SERIES-WISE MCCOY RINGS

Let $R$ be a ring with an endomorphism $\alpha$‎. ‎A ring $R$ is a skew power series McCoy ring if whenever any non-zero power series $f(x)=\sum_{i=0}^{\infty}a_ix^i,g(x)=\sum_{j=0}^{\infty}b_jx^j\in R[[x;\alpha]]$ satisfy $f(x)g(x)=0$‎, ‎then there exists a non-zero element $c\in R$ such that $a_ic=0$‎, ‎for all $i=0,1,\ldots$‎. ‎We investigate relations between the skew power series ring and the standard ring-theoretic properties‎. ‎Moreover‎, ‎we obtain some characterizations for skew power series ring $R[[x;\alpha]]$‎, ‎to be McCoy‎, ‎zip‎, ‎strongly \textit{AB} and has Property (A)‎.