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MP-injective rings and MGP-injective rings

Author

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  • Zhanmin Zhu

    (Jiaxing University)

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.

Suggested Citation

  • Zhanmin Zhu, 2010. "MP-injective rings and MGP-injective rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(5), pages 627-645, October.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:5:d:10.1007_s13226-010-0036-7
    DOI: 10.1007/s13226-010-0036-7
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