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- W2398103208 abstract "Abstract. In this paper we study the regularity of inside (or outside)(θ,φ)-derivations in BCI-algebras X and provethat let d (θ,φ) :X → Xbe an inside (θ,φ)-derivation of X. If there exists a ∈ X such thatd (θ,φ) (x)∗ θ(a) = 0, then d (θ,φ) is regular for all x ∈ X. It is alsoshownthatifX isaBCK-algebra,theneveryinside(oroutside)(θ,φ)-derivation of X is regular. Furthermore the concepts of θ-ideal, φ-idealand invariant inside (or outside) (θ,φ)-derivations of X are introducedand their related properties are investigated. Finally we obtain the fol-lowingresult: Ifd (θ,φ) :X → X isanoutside(θ,φ)-derivationofX,thend (θ,φ) isregularifandonlyifevery θ-idealofX isd (θ,φ) -invariant. 1. IntroductionThroughout the present paper X will denote a BCI-algebra unless otherwisementioned. Jun and Xin [4] defined the notion of derivation on BCI-algebrasas follows: A self map d : X → X is called a left-right derivation (briefly an(l,r)-derivation) of X if d(x ∗ y) = d(x) ∗ y ∧ x ∗ d(y) holds for all x,y ∈ X.Similarly, a self map d : X → X is called a right-left derivation (briefly an (r,l)-derivation) of X if d(x∗y) = x∗d(y)∧d(x)∗y holds for all x,y ∈ X. Moreover,if d is both (l,r)- and (r,l)-derivations, it is a derivation on X. Following [11],a self map d" @default.
- W2398103208 created "2016-06-24" @default.
- W2398103208 creator A5035644463 @default.
- W2398103208 date "2016-04-30" @default.
- W2398103208 modified "2023-09-27" @default.
- W2398103208 title "REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS" @default.
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- W2398103208 doi "https://doi.org/10.4134/ckms.2016.31.2.229" @default.
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