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**Left WMC2 rings.**
*(English)*
Zbl 1221.16005

Summary: We introduce in this paper the concept of left WMC2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left HI rings can be extended to left WMC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on strongly regular rings.

### MSC:

16D80 | Other classes of modules and ideals in associative algebras |

16D25 | Ideals in associative algebras |

16E50 | von Neumann regular rings and generalizations (associative algebraic aspects) |

16D50 | Injective modules, self-injective associative rings |

### Keywords:

injective maximal left ideals; left idempotent reflexive rings; regular left self-injective rings; strongly regular rings
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\textit{J. Wei}, Int. J. Math. Math. Sci. 2011, Article ID 294301, 8 p. (2011; Zbl 1221.16005)

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### References:

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