  It is well known that every MV-algebra can be converted into a residuated
lattice satisfying divisibility and the double negation law. In our previous
papers we introduced the concept of an NMV-algebra which is a non-associative
modification of an MV-algebra. The natural question arises if an NMV-algebra
can be converted into a residuated structure, too. Contrary to MV-algebras,
NMV-algebras are not based on lattices but only on directed posets and the
binary operation need not be associative and hence we cannot expect to obtain a
residuated lattice but only an essentially weaker structure called a
conditionally residuated poset. Considering several additional natural
conditions we show that every NMV-algebra can be converted in such a structure.
Also conversely, every such structure can be organized into an NMV-algebra.
Further, we study a bit more stronger version of an algebra where the binary
operation is even monotonous. We show that such an algebra can be organized
into a residuated poset and, conversely, every residuated poset can be
converted in this structure.
