On the structure of complete \(\nu\)-normal primitive rings and its applications
A structure theorem for primitive rings with non-zero socles was established by N. Jacobson. In this paper, the notions of normal primitivity and simplicity for rings are generalized to \(\nu\)-normal primitivity and \(\nu\)-simplicity. The structure of these rings is thoroughly investigated and the well-known Utumi-Faith theorem is therefore extended to infinite matrix form. Also, Goldie prime rings with right Goldie dimension are extended to the infinite case. Information for complete rings of continuous linear transformations in a vector space over a division ring is provided. Primitive rings with \(\aleph_{\nu}\)- fold transitivity are studied.
complete rings of continuous linear transformations
scientific article; zbMATH DE number 4079653