The article examines the role of Gabriel filters of ideals in the ontext of semiprimef-rings. It is shown that for every 2-convex semiprimef-ringAand every multiplicative filter B of dense ideals the ring of quotients of A by B, namely the direct limit of the HomA(I, A) over allI∈ B, is anl-subring ofQA, the maximum ring of quotients. Relative to the category of all commutative rings with identity, it is shown that for every 2-convex semiprimef-ringAqA, the classical ring of quotients, is the largest flat epimorphic extension ofA. IfAis also a Prüfer ring then it follows that every extension ofAin qA is of the formS-1A for a suitable multiplicative subsetS. The paper also examines when a Utumi ring of quotients of a semiprimef-ring is obtained from a Gabriel filter. For a ring of continuous functionsC(X), withXcompact, this is so for eachC(U) andC*(U), whenUis dense open, but not for an arbitrary direct limit ofC(U),taken over a filter base of dense open sets. In conclusion, it is shown that, for a complemented semiprimef-ringA, the ideals ofAwhich are torsion radicals with respect to some hereditary torsion theory are precisely the intersections of minimal prime ideals ofA.