Let A⊆B be a ring extension and G set of A-submodules B. We introduce class closure operations on (which we call multiplicative (A,B,G)) that generalizes the classes star, semistar semiprime operations. study how Mult(A,B,G) these varies when A, B or vary, behaves under homomorphisms. As an application, show to reduce star analytically unramified one-dimensional Noetherian domains closures fini...