MP-injective rings and MGP-injective rings

Zhanmin Zhu ()
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Zhanmin Zhu: Jiaxing University

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 5, 627-645

Abstract: 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.

Keywords: MP-injective rings; MGP-injective rings; perfect rings; semiprime rings (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0036-7

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