• 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.

• 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.

• 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.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.16 no.5
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• pp.107-111
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• 2006

We analyze Domingo-Feller's first privacy homomorphism scheme with known-plaintext attack As a result, it is possible to get the secret key if we blow two known plaintext-ciphertext pairs when modulus n is public, and three or more pairs are sufficient when modulus n is secret.

• 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.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.273-278
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• 1997

Let A be a Banach algebra and B a semisimple annifilator Banach algebra. Then every homomorphism from A into B with range is continuous. Also we obtain condition s for the automatic continuity of homomorphism with dense range.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.31-36
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• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).