2022/12/29 by A. A. Tuganbaev, Tuganbaev, A. A.
Mathematics · #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2212.14172
Let A be a ring with minimum condition on principal right ideals. It is proved that ℵ0-distributive right (left) A-modules coincide with Artinian (Noetherian) right (left) A-modules. Rings, over which all right modules are direct sums of ℵ0-distributive coincide with rings of of finite representation type. Rings, whose right modules are semidistributive, coincide with Kawada rings, over basis rings of which all right modules are completely cyclic. The studies of Tuganbaev are supported by Russian Scientific Foundation, project 22-11-00052.