• Honam Mathematical Journal
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• v.27 no.4
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• pp.583-593
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• 2005

The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [2], [3], [9], [11], [12]. We find the derivation group $Der_{non}({\overline{WN_{1,0,0_{[2]}}})$ the non-associative simple algebra ${\overline{WN_{1,0,0_{[2]}}}$.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.415-421
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• 2020

In the proof of Theorem 3 on p.253 in [4], both right and left distributivity are assumed simultaneously which makes the proof invalid. We give a corrected proof for this theorem by introducing an extension of Lemma 2.2 in [2].

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.885-898
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• 2012

Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.537-547
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• 2011

In this article, we propose an estimation procedure for the treatment eect for the right censored data. We apply the least square method for deriving the estimation equation and obtain an explicit formula for an estimation. Then we consider some asymptotic properties with derivation of the asymptotic normality for the estimate. Finally we illustrate our procedure with an example and discuss some interesting aspects for the estimation procedure.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.37-44
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• 2018

We prove some theorems showing that a right Jordan ideal or a left Jordan ideal of a 3-prime near-ring must be commutative if it admits a nonzero derivation acting as a homomorphism or an antihomomorphism. Moreover, we give examples proving necessity of the conditions given.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.467-480
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• 2010

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra (see [2], [3], [4], [5], [6], [10], [13], [15], [16]). We and all the derivations of the growing algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)[1] with the set of all right annihilators $T_3$ = $\{id,\;\partial_1,\;\partial_2,\;\partial_3\}$ in the paper. The dimension of $Der_{non}$(WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$) of the algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is one and every derivation of the algebra WN($e^{{\pm}x_1x_2x_3}$, 0, 3)$_{[1]}$ is outer. We show that there is a class P of purely outer algebras in this work.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1127-1133
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• 2014

Let S be a nonempty subset of a ring R. A map $f:R{\rightarrow}R$ is called strong commutativity preserving on S if [f(x), f(y)] = [x, y] for all $x,y{\in}S$, where the symbol [x, y] denotes xy - yx. Bell and Daif proved that if a derivation D of a semiprime ring R is strong commutativity preserving on a nonzero right ideal ${\rho}$ of R, then ${\rho}{\subseteq}Z$, the center of R. Also they proved that if an endomorphism T of a semiprime ring R is strong commutativity preserving on a nonzero two-sided ideal I of R and not identity on the ideal $I{\cup}T^{-1}(I)$, then R contains a nonzero central ideal. This short note shows that the conclusions of Bell and Daif are also true without the additivity of the derivation D and the endomorphism T.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.191-207
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• 2015

Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, ${\alpha}$ is the associated automorphism of $\mathcal{G}$, f($x_1$, ${\cdots}$, $x_n$) is a non-central multilinear polynomial over $\mathcal{C}$ with n non-commuting variables and $$\mathcal{S}=\{f(r_1,{\cdots},r_n)\left|r_1,{\cdots},r_n{\in}\mathcal{R}\}$$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x{\in}\mathcal{R}$, or $\mathcal{G}={\alpha}$.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.73-81
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• 2021

Let R be a prime ring, Qr be the right Martindale quotient ring and C be the extended centroid of R. If �� be a nonzero generalized skew derivation of R and f(x1, x2, ⋯, xn) be a multilinear polynomial over C such that (��(f(x1, x2, ⋯, xn)) - f(x1, x2, ⋯, xn)) ∈ C for all x1, x2, ⋯, xn ∈ R, then either f(x1, x2, ⋯, xn) is central valued on R or R satisfies the standard identity s4(x1, x2, x3, x4).

• Honam Mathematical Journal
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• v.30 no.2
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• pp.273-281
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• 2008

We define the Lie-admissible algebra NW$({\mathbb{F}}[e^{A[s]},x_1,{\cdots},x_n])$ in this work. We show that the algebra and its antisymmetrized (i.e., Lie) algebra are simple. We also find all the derivations of the algebra NW$(F[e^{{\pm}x^r},x])$ and its antisymmetrized algebra W$(F[e^{{\pm}x^r},x])$ in the paper.