Wei, Jun-Chao MC2 rings. (English) Zbl 1170.16006 Kyungpook Math. J. 48, No. 4, 651-663 (2008). 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. Cited in 1 Document 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) Keywords:left MC2 rings; left nil-injective modules; YJ-injective modules; left Goldie rings; simple singular left modules PDFBibTeX XMLCite \textit{J.-C. Wei}, Kyungpook Math. J. 48, No. 4, 651--663 (2008; Zbl 1170.16006) Full Text: DOI