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On derivations and generalized derivations of bitonic algebras

Yon Yong Ho (Division of Information and Communication Convergence Engineering, Mokwon University, Daejeon, Korea)
Özbal Şule Ayar (Faculty of Science and Letter, Department of Mathematics, Yaşar Üniversitesi, Izmir, Turkey)

We introduce the notion of bitonic algebras as a generalization of dual BCCalgebras, and define the notion of (r,l)-derivations, (l,r)-derivations and generalized (r,l) and (l,r)-derivations on the bitonic algebras. Then we study the properties of the derivations and the generalized derivations on the bitonic algebras and the commutative bitonic algebras. Finally, we show that every generalized derivation of commutative bitonic algebras is a derivation.

Keywords: bitonic algebras, commutative bitonic algebras, (r,l) and (l,r)-derivations, generalized (r,l) and (l,r)-derivations, generalized derivations