The maximum ring topology on the rational number field among those for which the sequence 1/n converges to zero

Zelenyuk, Protasov and Khromulyak have proven that each countable ring is complete with the ring topology which is maximum among those for which a certain T-sequence converges. We present some concrete examples of this situation on Q. In particular, we present the maximum ring topology on Q for which the sequence (1/n) converges to zero, and also the maximum ring topology on Q for which (1/pn) converges to zero, pn being the nth prime number.