JP Journal of Algebra, Number Theory and Applications
Volume 25, Issue 2, Pages 105 - 112
(June 2012)
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A NOTE ON MP-INJECTIVE RINGS AND MGP-INJECTIVE RINGS
Zhu Zhanmin
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Abstract: Let R be a ring. R is right MP-injective, if every R‑monomorphism from a principal right ideal of R to R extends to an endomorphism of R; R is right MGP-injective if, for any there exists a positive integer n such that and any R‑monomorphism from to R extends to an endomorphism of R. It is shown that (1) R is right FP-injective if and only if the full matrix ring is right MP-injective for every positive integer n if and only if the full matrix ring is right MGP-injective for every positive integer n; (2) If is right MGP-injective, then R is right MP-injective. |
Keywords and phrases: MP-injective rings, MGP-injective rings, FP-injective rings, matrix rings, trivial extensions. |
Communicated by Yuanlin Li |
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