• Honam Mathematical Journal
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• v.40 no.2
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• pp.227-237
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• 2018

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.227-236
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• 2006

Several authors find all the derivations of an algebra [1], [3], [7]. A Weyl type non-associative algebra and its sub algebra are defined in the paper [2], [3], [10]. All the derivations of the non-associative algebra $\overline{WN_{0,0,s1}$ is found in this paper [4]. We find all the derivations of the non-associative algebra $\overline{WN_{0,s,01}$ in this paper [5].

• Honam Mathematical Journal
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• v.36 no.3
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• pp.493-503
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• 2014

We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.247-259
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• 2016

We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.179-186
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• 2014

In this paper, we consider the simple non-associative algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$. There are many papers on finding the derivations of an associative algebra, a Lie algebra, and a non-associative algebra (see [2], [3], [4], [5], [6], [7], [12], [14]). We find all the derivations of the algebra $\overline{WN(\mathbb{F}[e^{{\pm}x^r},0,1]_{(\partial,\partial^2)})}$.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.269-277
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• 2016

In a paper of S. H. Choi [2], the author studied the derivations of a restricted Weyl Type non-associative algebra, and determined a 1-dimensional vector space of derivations. We describe all the derivations of this algebra and prove that they form a 3-dimensional Lie algebra.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.73-82
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• 2022

Let K be a field of characteristic zero. We first show that images of the linear derivations and the linear 𝓔-derivations of the polynomial algebra K[x] = K[x₁, x₂, …, x_n] are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear 𝓔-derivations are not unity. In addition, we prove that the images of D and 𝛿 are Mathieu-Zhao spaces of the polynomial algebra K[x] if D = ∑ⁿ_i=1 (a_ix_i + b_i)∂_i and 𝛿 = I - 𝜙, 𝜙(x_i) = λ_ix_i + 𝜇_i for a_i, b_i, λ_i, 𝜇_i ∈ K for 1 ≤ i ≤ n. Finally, we prove that the image of an affine 𝓔-derivation of the polynomial algebra K[x₁, x₂] is a Mathieu-Zhao space of the polynomial algebra K[x₁, x₂]. Hence we give an affirmative answer to the LFED Conjecture for the affine 𝓔-derivations of the polynomial algebra K[x₁, x₂].

• East Asian mathematical journal
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• v.25 no.1
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• pp.69-87
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• 2009

In this paper we characterize f-derivations of a BCI-algebra as well as its center.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.163-179
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• 2017

In this paper, we introduce the notion of left derivations of BCH algebras and investigate some properties of left derivations in a BCH-algebra. Moreover, we introduce the notions of fixed set and kernel set of derivations in a BCH-algebra and obtained some interesting properties in medial BCH-algebras. Also, we discuss the relations between ideals in a medial BCH-algebras.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.209-216
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• 2016

In this paper, we introduce the notion of symmetric bi-derivations of a B-algebra and investigate some related properties. We study the notion of symmetric bi-derivations of a 0-commutative B-algebra and state some related properties.