内同构环与内异环的结构

所有真子环都同构的结合环,称为内同构环,任两不同的子环都不同构的结合环,称为内异环.本文目的是给出内同构环与内异环的一些结构定理,从而基本上解决了Szasz F.A.提出的问题81:怎样的结合环,它的不同子环总不同构?

Structure of Inner Isomorphic and Inner Non-isomorphic Rings

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.