Multipliers in d-algebras

BCK and BCI-algebras, two classes of algebras of logic, were introduced by Imai and Iseki [1], Iseki [2] and Iseki and Tanaka [3] and have been extensively studied by various other researchers [4, 5]. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. In [6, 7] a wider class of abstract algebras was introduced by Q.P.Hu and X.Li.They have shown that the class of BCI-algebras is a proper subclass of the class of BCH-algebras. BCH-algebras have also been studied by Chaudhry and some other researchers [8-10]. The notion of d-algebras, another generalization of the notion of BCK-algebras, was introduced by Neggers and Kim [11]. They studied some properties of this class of algebras. Since then many researchers have extensively studied these algebras [12-16]. The study of multipliers have been made by various researchers in the context of C-algebras, rings and semigroups [17]. They have studied the properties of multipliers on them as well as properties of these algebraic structures using the notion of a multiplier on them. But the properties of multipliers o n d-algebras, an important class of algebras containing the class of BCK-algebras, have not been investigated so far. So with this motivation, in this paper we introduce the concept of a multiplier on a d-algebra and obtain some properties of multipliers of d-algebras.