On derivations of MV-algebras

TL;DR

This paper explores properties of derivations in MV-algebras, characterizes additive derivations, and reveals structural relationships, including isomorphisms and decompositions related to fixed point sets and Boolean algebra structures.

Contribution

It provides new characterizations of additive derivations, demonstrates that fixed point sets form MV-algebras, and establishes isomorphisms and structural decompositions involving Boolean derivations.

Findings

Fixed point set of additive derivations forms an MV-algebra

Fixed point sets of boolean additive derivations are isomorphic

Every MV-algebra decomposes into fixed point sets of boolean derivations

Abstract

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtain that the fixed point set of additive derivations is still an MV-algebra. Also, we study boolean additive derivations and their adjoint derivations. In particular, we get that the fixed point set of boolean addition derivations and that of their adjoint derivations are isomorphism. Moreover, we prove that every MV-algebras are isomorphic to the direct product of the fixed point set of boolean additive derivations and that of their adjoint derivations. Finally, Finally, we show that the structure of a Boolean algebra is completely determined by its set of all boolean additive (implicative) derivations.