Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to realm topological with right linear topology, we show that abelian category left contramodules over such a ring is split (equivalently, semisimple) if and only discrete modules same semisimple). Our results in this direction complement those Iovanov-Mesyan-Reyes. An extension Bass perfect formulated as list c...

Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...