In the present paper, we introduce the notion of generalized left derivation of a BCI-algebra X, construct several examples, and investigate related properties. Also establish some results on regular generalized left derivation. Furthermore, for a generalized left derivation H, the concept of a H-invariant generalized left derivation is introduced, and examples are discussed. Using this concept a condition for a generalized left derivation to be regular is provided. Finally, some results on p-semisimple BCI-algebra are obtained and it is shown that let H be a self map in a p-semisimple BCI-algebra X. Then H is a generalized left derivation if and only if it is a derivation on X.
Digital Object Identifier (DOI)
Muhiuddin, G. and M. Al-roqi, A.
"On Generalized Left Derivations in BCI-Algebras,"
Applied Mathematics & Information Sciences: Vol. 08
, Article 26.
Available at: https://dc.naturalspublishing.com/amis/vol08/iss3/26