Do Isomorphic Structural Matrix Rings Have Isomorphic Graphs?
نویسندگان
چکیده
We first provide an example of a ring R such that all possible 2 × 2 structural matrix rings over R are isomorphic. However, we prove that the underlying graphs of any two isomorphic structural matrix rings over a semiprime Noetherian ring are isomorphic, i.e. the underlying Boolean matrix B of a structural matrix ring M(B,R) over a semiprime Noetherian ring R can be recovered, contrary to the fact that in general R cannot be recovered.
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