• Honam Mathematical Journal
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• v.31 no.4
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• pp.601-609
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• 2009

The notion of generalized derivations of a BCI-algebra is introduced, and some related properties are investigated. Also, the concept of a torsion free BCI-algebra is introduced and some properties are discussed.

• East Asian mathematical journal
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• v.15 no.2
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• pp.165-176
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• 1999

After the derivation was defined in [19] by Posner a lot of researchers studied the derivations in ring theory in different manners such as in [2], [4], [5], ..., etc. Furthermore, many researches followed the definition of the generalized derivation([3], [6], [7], ..., etc.). Finally, Maksa defined a symmetric bi-derivation and many researches have been done in ring theory by using this definition. In this work, defining a symmetric bi-$\alpha$-derivation, we study the mentioned researches above in the light of this new concept.

• East Asian mathematical journal
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• v.30 no.3
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• pp.259-270
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• 2014

For a generalized triangular matrix ring $$T=\[\array{R\;M\\0\;S}]$$, over rings R and S having only the idempotents 0 and 1 and over an (R, S)-bimodule M, we characterize all homomorphisms ${\alpha}$'s and all ${\alpha}$-derivations of T. Some of the homomorphisms are compositions of an inner homomorphism and an extended or a twisted homomorphism.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.33-34
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• 2017

$Fo{\check{s}}ner$ [1] defined a module left (m, n)-derivation and proved the Hyers-Ulam stability of module left (m, n)-derivations. In this note, we prove that every module left (m, n)-derivation is trival if the algebra is unital and $m{\neq}n$.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.119-129
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• 2021

In this paper, we introduce the concept of a generalized right f-derivation associated with a derivation d and a function f in 𝚪-incline algebras and give some properties of 𝚪-incline algebras. Also, the concept of d-ideal is introduced in a 𝚪-incline algebra with respect to right f-derivations.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.387-393
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• 2021

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map D : X × X → X is a symmetric bi-derivation on X if and only if D is a symmetric map and it satisfies D(x - y, z) = D(x, z) - y for all x, y, z ∈ X.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.68-77
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• 2021

This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.353-361
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• 2024

We consider 𝒩 to be a 3-prime field and 𝒫 to be a prime ideal of 𝒩. In this paper, we study the commutativity of the quotient near-ring 𝒩/𝒫 with left multipliers and derivations satisfying certain identities on 𝒫, generalizing some well-known results in the literature. Furthermore, an example is given to illustrate the necessity of our hypotheses.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.1-10
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• 2024

In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.417-432
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• 2024

In this research article, we study a class of semirings with involution. Differential identities involving two or three derivations of a semiring with second kind involution are investigated. It is analyzed that how these identities, with a special role for second kind involution, bring commutativity to semirings.