A Note on א0-injective Rings
نویسنده
چکیده
A ring R is called right א0-injective if every right 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 semiperfect, then R is right א0injective 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 looked as an approach to the Faith-Menal conjecture.
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