A note on small rings
The author generalizes several results of the reviewer [Sitzungsber., Bayer. Akad. Wiss., Math.-Naturwiss. Kl. 1965, 185-199 (1966; Zbl 0207.327)] on Dedekind domains to finite direct sums \(R=R_ 1\oplus...\oplus R_ n\) of such. Among the proper commutative domains \(R_ i\) the Dedekind domains are characterized by the fact that R-modules are injective iff they coincide with their Jacobson radicals, or by the fact that finitely generated R-modules with zero socle are projective. The author uses some results on rings which are small (superfluous) modules (in their injective hulls).
scientific article; zbMATH DE number 4029712
scientific article