### fq-Derivations of b-algebras

#### Abstract

Let X = (X,∗,0) be a B-algebra and f a self-map on X. We study some properties of X for the self-map d f q is an outside and inside fq-derivation of X, respectively, as follows:

(∀x, y ∈ X)(d^{f}_{q}(x ∗ y) = f(x) ∗ d^{f}_{q} (y)),

(∀x, y ∈ X)(d^{f}_{q} (x ∗ y) = d^{f}_{q}(x) ∗ f(y)).

In addition, we define and study some properties of (right-left) and (left-right) fq-derivation of X, respectively, as follows:

(∀x, y ∈ X)(d^{f}_{q}(x ∗ y) = (f(x) ∗ d^{f}_{q}(y))∧(d^{f}_{q}(x) ∗ f(y))),

(∀x, y ∈ X)(d^{f}_{q}(x ∗ y) = (d^{f}_{q}(x) ∗ f(y))∧(f(x) ∗ d^{f}_{q}(y))).

**Published:**2021-03-10

**How to Cite this Article:**Patchara Muangkarn, Cholatis Suanoom, Ponchita Pengyim, Aiyared Iampan, fq-Derivations of b-algebras, J. Math. Comput. Sci., 11 (2021), 2047-2057 Copyright © 2021 Patchara Muangkarn, Cholatis Suanoom, Ponchita Pengyim, Aiyared Iampan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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