Radicals in the class of compact right topological rings. (Q2922059)

The paper deals with the class of compact right topological rings, the definition of which is not provided (there is only a hint, that this definition could be obtained from another paper). For the sake of understanding the topic better, the reviewer remarks that a right topological ring is a ring equipped with the topology in which the right multiplication is continuous (but the left multiplication might be discontinuous).NEWLINENEWLINE In this paper it is shown that all compact right topological simple Artinian rings of prime characteristic and all simple left Noetherian unital compact right topological rings of prime characteristic are finite. It is also shown that the operator which sends each compact right topological ring to the intersection of all of its open maximal ideals, is a radical in the class of all compact right topological rings.