B737 FLT CREW HAS RWY INCURSION AT OMA.

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I LANDED RWY 14R AT OMA. WET RWY. I INITIATED BRAKING AT 80 KIAS. AFTER BRAKING TO LESS THAN APPROX 30 KIAS; THE CAPT CAME ON THE BRAKES AND WE INITIATED SMOOTH XFER OF CTL OF THE ACFT. PASSING TXWY C; TWR SAID 'EXIT RWY AT TXWY C.' AT TAXI SPD; WE WERE ALREADY PASSING TXWY C AND WE EXITED ONTO RWY 18 AT THE INTXN OF RWYS 14R AND 18. WHILE TURNING ONTO RWY 18; I IMMEDIATELY CAME ON THE RADIO TO SEE IF WE COULD TAXI ONTO RWY 18. THE TWR REPLIED TO THE EFFECT; 'TAXIING ONTO AN ACTIVE RWY REQUIRED ATC APPROVAL.' I IMMEDIATELY APOLOGIZED AND ASKED IF WE CAUSED A PROB AND IF THERE WAS ANY PROB. TWR RESPONDED; 'NO PROB.' IN HINDSIGHT; WE BRIEFED THE LNDG RWY FOR THE QUICKEST AND MOST EFFICIENT LNDG AND TAXI. WE DISCUSSED TXWY C TURNOFF BUT NOT RWY 18. IN HINDSIGHT; LOOKING AT THE DIAGRAM OF THE AIRFIELD ON THE ARPT PAGE; TXWY C APPEARS TO BE AT THE INTXN OF RWYS 14R AND 18. ACTUALLY; THE INTXN IS 100 FT PAST TXWY C AND I THINK THERE WAS AN INSTINCTIVE INITIATING OF THE TURNOFF AT THE INTXN ASSUMING THAT TXWY C WAS THERE. AFTER INITIATING THE TURNOFF; WE WERE COMMITTED. THIS WAS NOT A HURRIED ACTION TO LAND AND BRAKE QUICK FOR THE TURNOFF. BRAKING DECREATION WAS NORMAL AND DELIBERATE WITH CONSIDERATION FOR PAX COMFORT. WE WERE SURPRISED INITIALLY THAT TXWY C WAS NOT AT THE INTXN AND COMING TO A FULL STOP WITH A RADIO CALL TO TWR WOULD HAVE ALLEVIATED THE CONFLICT.