This paper sets forth the foundations for a transactional approach for the performance of arbitrage in foreign exchange markets. Firstly, we review both the standard model of financial arbitrage and the so-caled covered-interest arbitrage environment, and we also lay bare striking shortcomings in these points of view, mainly grounded on a wide- ranging empirical evidence. Next, we move on to what we have labeled in previous research working papers a transactional algebra, from which we expand on its main tools of analysis, namely differential rates, residual information sets, arbitrage gaps and transaction costs functions. Afterwards, we establish and prove the minimal conditions under which a successful arbitrage can be carried out within a transactional algebra.