On topologies over rings (Q1063677)

The paper deals with the topological rings which have bases of neighbourhoods of zero consisting of right ideals. A topology \({\mathcal T}\) on the ring R is called a Gabriel topology if it satisfies the condition: if \({\mathcal I}\subset {\mathcal J}\), where \({\mathcal I}\) and \({\mathcal J}\) are right ideals in R, \({\mathcal J}\in {\mathcal T}\) and (\({\mathcal I}:a)\in {\mathcal T}\) for every \(a\in {\mathcal J}\), then \({\mathcal I}\in {\mathcal T}\). The author partially answers the question concerning the description of the smallest Gabriel topology \({\mathcal T}'\) which contains the topology \({\mathcal T}\). The result obtained by the author includes the case of right Noetherian rings.