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von Neumann regularity of similar \(N\)-rings. (Chinese. English summary) Zbl 1141.16013

Summary: The similar \(N\)-rings are defined. Some fundamental properties are given. It is shown that for a similar \(N\)-ring \(R\), the following conditions are equivalent: (1) \(R\) is a strongly regular ring; (2) each left (right) \(R\)-module is a YJ-injective module; (3) \(R\) is left (right) P-injective; (4) \(R\) is a left (right) SF-ring.

MSC:

16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
16D50 Injective modules, self-injective associative rings
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