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MP-injective rings and MGP-injective rings

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Abstract

A ring R is said to be right MP-injective if every monomorphism from a principal right ideal to R extends to an endomorphism of R. A ring R is said to be right MGP-injective if, for any 0 ≠ a ∈ R, there exists a positive integer n such that a n ≠ 0 and every monomorphism from a n R to R extends to R. We shall study characterizations and properties of these two classes of rings. Some interesting results on these rings are obtained. In particular, conditions under which right MGP-injective rings are semisimple artinian rings, von Neumann regular rings, and QF-rings are given.

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Authors and Affiliations

  1. Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang Province, 314001, Peoples’ Republic of China

    Zhanmin Zhu

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  1. Zhanmin Zhu
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Correspondence to Zhanmin Zhu.

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Zhu, Z. MP-injective rings and MGP-injective rings. Indian J Pure Appl Math 41, 627–645 (2010). https://doi.org/10.1007/s13226-010-0036-7

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  • DOI: https://doi.org/10.1007/s13226-010-0036-7

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