In this paper we revise the Lukasiewicz implication prealgebras which we will call Lukasiewicz I?prealgebras to sum up. They were used by Antonio Jes′us Rodríguez?Salas on his doctoral thesis under the name of Sales prealgebras. These structures are a?natural generalization of the notion of I?prealgebras, introduced by A. Monteiro in 1968?aiming to study using algebraic techniques the {!}-fragment of the three-valued Lukasiewicz?propositional calculus. The importance of Lukasiewicz I?prealgebras focuses on the fact that?from these structures we can directly prove that Lindembaun-Tarski algebra in the {!}- fragment of the infinite-valued Lukasiewicz implication propositional calculus is a Lukasiewicz?residuation BCK-algebra in the sense of Berman and Blok [1]. This last result is indicated?without a proof on Komori’s paper ([8]) and it is suggested on his general lines on the Rodriguez?Salas thesis.
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