
TL;DR
This paper studies J-regular rings, showing their properties related to right injectivity and extending known results about their structure and injective modules.
Contribution
It establishes new characterizations of right n-injectivity and FP-injectivity in J-regular rings, improving existing results.
Findings
R is right n-injective iff certain homomorphisms extend
R is right FP-injective iff it is right (J, R)-FP-injective
Improves known results on J-regular rings
Abstract
A ring 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 -generated small right ideal of to can be extended to one from to ; (ii) R is right FP-injective if and only if R is right (J, R)-FP-injective. Some known results are improved.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models
