Asian Journal of Mathematics and Computer Research

A NOTE ON FP-INJECTIVE RINGS

ZHANMIN ZHU *

Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang Province, 314001, P.R. China.

*Author to whom correspondence should be addressed.

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Abstract

In this note, we give a new characterization of FP-injective rings. Namely, we show that: A ring R is right FP-injective if and only if every homomorphism from a nitely generated submodule of a free right R-module F to R with principal image can be extended to a homomorphism from F to R.

Keywords: FP-injective ring, F-injective ring, (m, n)-injective ring, n-injective ring.

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