Let R be a ring with an endomorphism α and R[x;α] 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.
