The topological Jacobson radical of rings. II

In this paper, topologically primitive rings and rings possessing a faithful topologically irreducible module and being bounded by this module are considered for the investigation of properties of their topological Jacobson radical. We investigate the topological Jacobson radical in some classes of topological rings such as left topologically Artinian rings, topological rings possessing a basis of neighborhoods of zero consisting of ideals, compact rings, bounded strictly linearly compact rings.