Abstract: To discuss the various extension properties of feckly McCoy rings and feckly Armendariz rings, it is proved that(1)let R be a feckly Armendariz ring with J(R［x］)=J(R)［x］, if for each principal right ideal pR⊈J(R), rJR(pR)=aR where a∈J(R), then for each principal right ideal f(x)R［x］⊈J(R［x］), rJ_R［x］(f(x)R［x］)is generated as an ideal by an element which is in the Jacobson radical of R［x］. (2)let R be a feckly reduced ring with J(R［x］)=J(R)［x］, R is a right J-APP-ring if and only if R［x］ is a right J-APP-ring. These deepen the study of these two new classes of rings.

Key words: feckly McCoy ring, feckly Armendariz ring, feckly reduced ring, extension of ring