on skew armendariz ideals of rings

Let $r$ be a ring with an endomorphism $alpha$ and $r[x; alpha]$ be the ring of skew polynomials. in this paper we study the skew armendariz property on ideals of rings, introducing a new concept which unifies the various armendariz properties for rings. ##a ring $r$ is weak skew armendariz if and only if every left ideal of $r$ is weak skew armendariz. ##we determine weak skew armendariz ideals of some ring extensions and study related properties