On Generalized Left Derivations in BCI-Algebras
نویسندگان
چکیده
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 .
منابع مشابه
MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS
Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations from the triangular Banach algebraof t...
متن کاملFixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras
In this paper, using fixed point method, we prove the generalized Hyers-Ulam stability of random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for the following $m$-variable additive functional equation: $$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...
متن کاملFuzzy Derivations BCC-Ideals on BCC-Algebras
In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introd...
متن کاملOn the stability of generalized derivations on Banach algebras
We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.
متن کاملOn Symmetric Left Bi-Derivations in BCI-Algebras
The notion of symmetric left bi-derivation of a BCI-algebra X is introduced, and related properties are investigated. Some results on componentwise regular and d-regular symmetric left bi-derivations are obtained. Finally, characterizations of a p-semisimple BCI-algebra are explored, and it is proved that, in a p-semisimple BCI-algebra, F is a symmetric left bi-derivation if and only if it is a...
متن کامل