Topologies de corps A linéaires (Q801123)

For every prime ideal P of an integral domain A the P-adic topology of the field of quotients K of A means the topology in which the system of nonzero A-submodules of K forms a basis of neighbourhoods of zero of K. A ring A is called topological Prüfer if every P-adic topology on A is a valuation one. The paper deals with such rings. Particularly sufficient conditions are found for a topological Prüfer ring to satisfy the upper bound property, i.e. every field A-linear topology on K has as upper bound the family of P-adic topologies, where P is a prime ideal of A. \(\{\) Joint review with P. Kirku\(\}\).