On t-derivations of PMS-algebras

Background PMS algebras are a type of algebraic structure that has been studied extensively in recent years. They are a generalization of several other algebraic structures, such as Boolean algebras and MV-algebras. Methods In this paper, we introduce the concept of t-derivations on PMS algebras. T-derivations are a type of mapping between PMS algebras that satisfies certain properties. We then study the properties of t-derivations and regular t-derivations on PMS algebras. Results We characterize further properties of t-derivations in the context of PMS algebras. We also investigate a novel result of t-derivations on the G-part of a PMS-algebra. Finally, we prove that the set of all t-derivations on a PMS-algebra forms a semigroup. Conclusions This paper provides a comprehensive study of t-derivations on PMS algebras. We have established several new results and characterized the properties of t-derivations in detail. Our results contribute to the further understanding of PMS algebras and their associated structures.