ON SYMMETRIC BI-GENERALIZED DERIVATIONS OF LATTICE IMPLICATION ALGEBRAS

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map F : L × L → L is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies F(x → y, z) = x → F(y, z) for all x, y, z ∈ L.