# Some results on derivations of MV-algebras

Some results on derivations of MV-algebras In this paper, we review some of their related properties of derivations on MV-algebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic. In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive (implicative) derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97–113] and [Information Sciences, 178(2008), 307–316]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

# Some results on derivations of MV-algebras

, Volume 38 (1) – Mar 1, 2023
18 pages      /lp/springer-journals/some-results-on-derivations-of-mv-algebras-J95T0YRHja
Publisher
Springer Journals
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-023-4054-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we review some of their related properties of derivations on MV-algebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic. In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive (implicative) derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97–113] and [Information Sciences, 178(2008), 307–316].

### Journal

Applied Mathematics-A Journal of Chinese UniversitiesSpringer Journals

Published: Mar 1, 2023

Keywords: MV-algebra; derivation; fixed point set; ideal; Boolean algebra; 06B35; 06B99

Access the full text.