A concept of largeness of CR-sets

Let A be a u v matrix with rational entries. In key-6 N. Hindman and D. Strauss determined several characterizations of the property that whenever B is piecewise syndetic (J-set) in Z, \ x^{v: Ax B^u\} is piecewise syndetic (J-set) in Z^v. In key-1 V. Bergelson and D. Glasscock introduced combinatorially Rich sets (denoted CR-sets). Assume that for each a, there exists x^v such that Ax=a^u. In this article, we prove that \ y^{v: Ay B^u\} is a CR-set in Z^v if B is CR-set in Z.