Structure of Inner Isomorphic and Inner Non-isomorphic Rings

Abstract:

      An associative ring R is called an inner isomorphic, if any two proper sub-rings of it are isomorphic. An associative ring R is called an inner nonisomor-phic, if the distinct subrings of it are always non-isomorphic. In this paper, we obtain several structure theorems of inner isomorphic and inner non-isomor-phic ring, so that totally solve the open problem 81 provided by F. A. Szasz who asks "in which ring are the distinct subrings always non-isomorphic?" [1] additional, we point out that the main results and its proofs in paper[2] are mistaken.