Generalizations of Derivations in BCI-Algebras

Authors

G. Muhiuddin, Department of Mathematics, University of Tabuk, P. O. Box 741, Tabuk 71491, Saudi ArabiaFollow
Abdullah M. Al-roqi, Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaFollow

Author Country (or Countries)

Saudi Arabia

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090113

Recommended Citation

Muhiuddin, G. and M. Al-roqi, Abdullah (2023) "Generalizations of Derivations in BCI-Algebras," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 20.
DOI: http://dx.doi.org/10.12785/amis/090113
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/20