\documentclass[12pt]{article} \begin{document} \title{A non-commutative generalization of $MV$-algebras} \author{Ji\v r\'\i\ Rach\accent23 unek, Palack\'y University Olomouc} \date{} \maketitle $MV$-algebras have been introduced by C. C. Chang as an algebraic counterpart of the \L ukasiewicz infinite valued propositional logic. By D. Mundici, every $MV$-algebra can be viewed as an interval of an abelian lattice ordered group. Moreover, by J. Rach\accent23 unek, $MV$-algebras can be considered as special cases of bounded dually residuated commutative lattice ordered monoids. We introduce a non-commutative generalization of the concept of an $MV$% -algebra and describe a one-to-one correspondence between generalized $MV$% -algebras and some bounded non-commutative dually residuated lattice ordered monoids. Further we compare generalized $MV$-algebras with intervals of lattice ordered groups and loops. \end{document}