A topological ring$R$ is said to have a (left) linear topology if it has a topological base of neighbourhoods of 0 consisting of (left) ideals.

Taking this apart we have a definition/proposition of such a topology, given by a left uniform filter:

Proposition (Gabriel)

A nonempty family of left ideals in $R$ is a left uniform filter (=topologizing filter) of left ideals iff it is a basis of neighborhood of $0$ of some left linear topology. In other words, the following conditions hold: