A ring R is called: Right FIP: if for all of R, there exists a finite subset of X such that . Right G-FIP: if for all of R, there exists a finite subset of R such that . Right Zip: if for all of R with , there exists a finite subset of X such that . One of the important question on the Zip condition is: “When is the ring Zip where A is a H-module K-algebra over a Hopf algebra H?” The behaviors of the above rings properties (especially Zip property) under some ring. Constructions are studied. Inparticular, actions of Hopf algebra, ring of quotients and certain subrings of matrix rings. A generalizations of this concents to modules with some applications are also given.