• 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.

• 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.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.641-655
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• 2022

A right R-module N is called pseudo semisimple-M-injective if for any monomorphism from every semisimple submodule of M to N, can be extended to a homomorphism from M to N. In this paper, we study some properties of pseudo semisimple-injective modules. Moreover, some results of pseudo semisimple-injective modules over formal triangular matrix rings are obtained.