• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.2
• /
• pp.227-236
• /
• 2014

In this paper, we introduce the notion of a generalized derivation in a BE-algebra, and consider the properties of generalized derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by generalized derivations. Moreover, we prove that if d is a generalized derivation of a BE-algebra, every filter F is a d-invariant.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.721-739
• /
• 2018

In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.67-79
• /
• 2009

We establish the generalized Hyers-Ulam-Rassias stability of higher ring derivations. Furthermore, we use the superstability of higher ring derivations to obtain approximately higher linear derivations mapping into the Jacobson radical under some conditions.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.505-517
• /
• 2014

We prove that every Jordan higher left (right) centralizer on a 2-torsion free semiprime ring is a higher left (right) centralizer which is to generalize the result of Zalar [18].

• The Pure and Applied Mathematics
• /
• v.13 no.4 s.34
• /
• pp.303-310
• /
• 2006

M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.535-542
• /
• 2017

Let R be an associative ring and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an (${\alpha},{\beta}$)-derivation of R if $d(xy)=d(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $D:R{\rightarrow}R$ is called a generalized (${\alpha},{\beta}$)-derivation of R associated with an (${\alpha},{\beta}$)-derivation d if $D(xy)=D(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [5], and a theorem of Daif and El-Sayiad [2].

• Journal of the Chungcheong Mathematical Society
• /
• v.16 no.1
• /
• pp.97-101
• /
• 2003

We investigate generalized Baxter equations on Banach algebras. This is applied to understand generalized anti-derivations on Banach *-algebras.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.2
• /
• pp.251-258
• /
• 2017

The aim of the present paper is to establish some results involving generalized ${\ast}$-derivations in ${\ast}$-rings and investigate the commutativity of prime ${\ast}$-rings admitting generalized ${\ast}$-derivations of R satisfying certain identities and some related results have also been discussed.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.3
• /
• pp.307-318
• /
• 2020

In this paper, we extend the notion of a generalized derivation F associated with derivation d to two generalized derivations F and G associated with the same derivation d, as a new idea, to obtain the commutativity of prime rings under certain conditions.

• Kyungpook Mathematical Journal
• /
• v.57 no.1
• /
• pp.125-132
• /
• 2017

We obtain commutativity-free characterizations of higher derivations on a unital Banach algebra that map into its Jacobson radical. We also investigate the spectral boundedness of generalized higher derivations.