(⊙,∨)-Derivations on MV-algebras

Let A be an MV-algebra. An (circle dot,boolean OR)-derivation on A is a map d : A -> A satisfying: d(x circle dot y) = (d(x) circle dot y) boolean OR (x circle dot d(y)) for all x, y is an element of A. This paper initiates the study of (circle dot,boolean OR)-derivations on MV-algebras. Several families of (circle dot,boolean OR)-derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (circle dot,boolean OR)-derivations. Furthermore, (circle dot,boolean OR)-derivations on a finite MV-chain are enumerated and the underlying lattice is described.