The Enumeration of (⊙,∨)-Multiderivations on a Finite MV-Chain

Abstract

In this paper, (⊙,∨)-multiderivations on an MV-algebra A are introduced, the relations between (⊙,∨)-multiderivations and (⊙,∨)-derivations are discussed. The set MD(A) of (⊙,∨)-multiderivations on A can be equipped with a preorder, and (MD(A)/∼,≼) can be made into a partially ordered set with respect to some equivalence relation ∼. In particular, for any finite MV-chain Ln, (MD(Ln)/∼,≼) becomes a complete lattice. Finally, a counting principle is built to obtain the enumeration of MD(Ln).