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Generalizations of Derivations in BCI-Algebras |
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PP: 89-94 |
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Author(s) |
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G. Muhiuddin,
Abdullah M. Al-roqi,
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Abstract |
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| 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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