2007/10/30 by Liang Shen, Shen, Liang
Mathematics · #16D50 #16L60 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16D50 #msc:16L60
paper · pdf · doi:10.48550/arxiv.0710.5565
10 pages
openalex publication_date 2007/10/30 · arxiv created 2010/05/23 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A ring R is called right ℵ0-injective if every homomorphism from a countably generated right ideal of R to RR can be extended to a homomorphism from RR to RR. In this note, some characterizations of ℵ0-injective rings are given. It is proved that if R is semilocal, then R is right ℵ0-injective if and only if every homomorphism from a countably generated small right ideal of R to RR can be extended to one from RR to RR. It is also shown that if R is right noetherian and left ℵ0-injective, then R is QF. This result can be considered as an approach to the Faith-Menal conjecture.