Researches on n-Morphic Rings

This article introduces the n-morphic rings. That is,every (left) n-morphic ring is a (left) π-morphic ring but conversely is not true. Several related results are also considered. 1) Some characteristics of left n-morphic elements in the corner ring of R are obtained. 2) Some examples of n-morphic but not (n-1)-morphic are constructed. 3) It considers the characteristics of n-morphic over the upper triangular matrices rings,and shows that the n×n upper triangular matrices rings of Z2 is not m-morphic where m is any positive integers less than n.