| Structure of Inner Isomorphic and Inner Non-isomorphic Rings |
| Received:November 20, 1989 |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1991.03.004 |
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