REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS

On Generalized Left Derivations in BCI-Algebras

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 concep...

Generalizations of Derivations in BCI-Algebras

In the present paper we introduced the notion of (θ ,φ)-derivations of a BCI-algebra X . Some interesting results on inside (or outside) (θ ,φ)-derivations in BCI-algebras are discussed. It is shown that for any commutative BCI-algebra X , every inside (θ ,φ)derivation of X is isotone. Furthermore it is also proved that for any outside (θ ,φ)-derivation d(θ ,φ) of a BCI-algebra X , d(θ ,φ)(x) =...

On α, β -Derivations in BCI-Algebras

On t-Derivations of BCI-Algebras

and Applied Analysis 3 Definition 2.2 see 6 . A subset S of a BCI-algebra X is called subalgebra of X if x ∗ y ∈ S whenever x, y ∈ S. For a BCI-algebra X, we denote x ∧ y y ∗ y ∗ x for all x, y ∈ X 6 . For more details we refer to 3, 5, 6 . 3. t-Derivations in a BCI-Algebra/p-Semisimple BCI-Algebra The following definitions introduce the notion of t-derivation for a BCI-algebra. Definition 3.1....

On f-derivations of BCI-algebras

In the theory of rings and near-rings, the properties of derivations are an important topic to study, see [2, 3, 7, 10]. In [6], Jun and Xin applied the notions in rings and nearrings theory to BCI-algebras, and obtained some related properties. In this paper, the notion of left-right (resp., right-left) f -derivation of a BCI-algebra is introduced, and some related properties are investigated....