BL-Algebras with Permuting Tri-Derivations

Abstract

Basic logic algebras (BL-algebras) were introduced by Hajek. Multi-value algebras (MV-algebras), Gödel algebras, and product algebras are particular cases of BL-algebras. Moreover, BL-algebras are algebraic structures, and their principal examples are the real interval $[0, 1]$ with the structure given by a continuous $t$-norm and abelian $l$-groups. In this article, we consider a type of derivation structure on BL-algebras. We study $(\odot,\vee)$-permuting tri-derivations of BL-algebras and their examples and basic properties. We obtain results regarding the trace of $(\odot,\vee)$-permuting derivations on Gödel BL-algebras. Finally, the article presents that the results herein can be generalized in future research.