J-regular rings with injectivities

Liang Shen

paper

J-regular rings with injectivities

arXiv:1004.0562

Abstract

A ring $R$ is called a J-regular ring if R/J(R) is von Neumann regular, where J(R) is the Jacobson radical of R. It is proved that if R is J-regular, then (i) R is right n-injective if and only if every homomorphism from an $n$ -generated small right ideal of $R$ to $R_{R}$ can be extended to one from $R_{R}$ to $R_{R}$ ; (ii) R is right FP-injective if and only if R is right (J, R)-FP-injective. Some known results are improved.

7 pages