• Honam Mathematical Journal
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• v.42 no.2
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• pp.411-423
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• 2020

In this paper, we correct some errors and typos of [2] and introduce a new concept related to pseudo n-Jordan homomorphisms, that we call it pseudo n-homomorphism. We investigate automatic continuity and positivity of pseudo n-homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras and C*-algebras. Moreover, we show that the sum of two pseudo n-Jordan homomorphisms is not a pseudo n-Jordan homomorphism and we show that under some conditions the sum of two pseudo n-Jordan homomorphisms is a pseudo n-Jordan homomorphism.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.737-744
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• 2021

In this paper, among other things, we show that under special hypotheses every [pseudo] (n + 1)-Jordan homomorphism is a [pseudo] n-Jordan homomorphism and vice versa.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.487-490
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• 2023

In this short note, we give a simple proof of the main theorem of [5] which states that every n-Jordan homomorphism h : A → B between two commutative algebras A and B is an n-homomorphism.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.31-35
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• 2020

With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A, B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.757-768
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• 2020

In this paper, the Hyers-Ulam-Rassias stability of mixed n-Jordan homomorphisms on Banach algebras and the superstability of mixed n-Jordan ∗-homomorphism between C∗-algebras are investigated.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.165-170
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• 2018

In this paper, we show that every unital n-Jordan homomorphism ${\varphi}$ from a Banach algebra ${\mathcal{A}}$ onto a semisimple commutative Banach algebra B is continuous.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2027-2034
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• 2013

In this article, it is proved that under some conditions every bijective Jordan triple product homomorphism from generalized matrix algebras onto rings is additive. As a corollary, we obtain that every bijective Jordan triple product homomorphism from $M_n(\mathcal{A})$ ($\mathcal{A}$ is not necessarily a prime algebra) onto an arbitrary ring $\mathcal{R}^{\prime}$ is additive.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.709-737
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• 2020

Let R be a prime ring of characteristic different from 2. Suppose that F, G, H and T are generalized derivations of R. Let U be the Utumi quotient ring of R and C be the center of U, called the extended centroid of R and let f(x₁, …, x_n) be a non central multilinear polynomial over C. If F(f(r₁, …, r_n))G(f(r₁, …, r_n)) - f(r₁, …, r_n)T(f(r₁, …, r_n)) = H(f(r₁, …, r_n)²) for all r₁, …, r_n ∈ R, then we describe all possible forms of F, G, H and T.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.253-260
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• 2005

Denote the set of n ${\times}$ n complex Hermitian matrices by Hn. A pair of n ${\times}$ n Hermitian matrices (A, B) is said to be rank-additive if rank (A+B) = rank A+rank B. We characterize the linear maps from Hn into itself that preserve the set of rank-additive pairs. As applications, the linear preservers of adjoint matrix on Hn and the Jordan homomorphisms of Hn are also given. The analogous problems on the skew Hermitian matrix space are considered.

• 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 $\mathcal{G}={\alpha}$.