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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 9 > No. 1


Generalizations of Derivations in BCI-Algebras

PP: 89-94
G. Muhiuddin, Abdullah M. Al-roqi,
In the present paper we introduced the notion of (q ,f )-derivations of a BCI-algebra X. Some interesting results on inside (or outside) (q ,f )-derivations in BCI-algebras are discussed. It is shown that for any commutative BCI-algebra X, every inside (q ,f )- derivation of X is isotone. Furthermore it is also proved that for any outside (q ,f )-derivation d(q ,f ) of a BCI-algebra X, d(q ,f )(x) = q (x)∧d(q ,f )(x) if and only if d(q ,f )(0) = 0 for all x ∈ X.

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