Abstract
Many researchers have studied permuting tri-derivation and generalized derivation in prime or semi-prime rings, BCK-algebras, lattices, d-algebras, MV-algebras and many algebraic structures. Later, they introduced the concept of generalized permuting tri-derivation by combining the concepts of generalized derivation and permuting tri-derivation. In this article, we have examined the properties of generalized permuting triderivation by adding conditions on their traces in prime or semi-prime rings. In addition, we examined the properties of two permuting triderivation by giving a relation between their traces.
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