Affiliation:
1. School of Mathematical Sciences, Shahe Campus, Beihang University, Beijing 102206, China
2. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022, China
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).
Reference30 articles.
1. Derivations in prime rings;Posner;Proc. Amer. Math Soc.,1957
2. Derivations of lattices;Acta Sci. Math.,1975
3. On derivations of lattices;Ferrari;Pure Math Appl.,2001
4. On derivations of lattices;Xin;Inf. Sci.,2008
5. The fixed set of a derivation in lattices;Xin;Fixed Point Theory Appl.,2012