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MC2 rings. (English) Zbl 1170.16006

Summary: We first study some characterizations of left MC2 rings. Next, by introducing left nil-injective modules, we discuss and generalize some well known results for a ring whose simple singular left modules are YJ-injective. Finally, as a byproduct of these results we are able to show that if \(R\) is a left MC2 left Goldie ring whose every simple singular left \(R\)-module is nil-injective and GJcp-injective, then \(R\) is a finite product of simple left Goldie rings.

MSC:

16D80 Other classes of modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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