Amalgamated algebra along an ideal defined by S-noetherian spectrum-like-conditions

Let f : A -> B be a ring homomorphism and J be an ideal of B. The subring A (sic)(f) J := {(a, f (a)+ j)/a is an element of A et j is an element of J} of A x B is called the amalgamation of A with B along with J with respect to f. In this paper we investigate a general concept of ring with Noetherian spectrum, called S-Noetherian spectrum property which was introduced by Hamed, on the A (sic)(f) J for a multiplicative subset S of A (sic)(f) J