• Korean Journal of Mathematics
• /
• 제25권2호
• /
• pp.163-179
• /
• 2017

In this paper, we introduce the notion of left derivations of BCH algebras and investigate some properties of left derivations in a BCH-algebra. Moreover, we introduce the notions of fixed set and kernel set of derivations in a BCH-algebra and obtained some interesting properties in medial BCH-algebras. Also, we discuss the relations between ideals in a medial BCH-algebras.

• 대한수학회논문집
• /
• 제17권2호
• /
• pp.245-252
• /
• 2002

In this paper we obtain some results concerning Jordan derivations and Jordan left derivations mapping into the Jacobson radical. Our main result is the following : Let d be a Jordan derivation (resp. Jordan left derivation) of a complex Banach algebra A. If d$^2$(x) = 0 for all x $\in$ A, then we have d(A) ⊆ red(A)

• 호남수학학술지
• /
• 제40권2호
• /
• pp.227-237
• /
• 2018

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

• 대한수학회논문집
• /
• 제21권2호
• /
• pp.227-236
• /
• 2006

Several authors find all the derivations of an algebra [1], [3], [7]. A Weyl type non-associative algebra and its sub algebra are defined in the paper [2], [3], [10]. All the derivations of the non-associative algebra $\overline{WN_{0,0,s1}$ is found in this paper [4]. We find all the derivations of the non-associative algebra $\overline{WN_{0,s,01}$ in this paper [5].

• 대한수학회논문집
• /
• 제28권4호
• /
• pp.697-707
• /
• 2013

In this paper, we introduce the notion of permuting $n$-derivations in near-ring N and investigate commutativity of addition and multiplication of N. Further, under certain constrants on a $n!$-torsion free prime near-ring N, it is shown that a permuting $n$-additive mapping D on N is zero if the trace $d$ of D is zero. Finally, some more related results are also obtained.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.801-812
• /
• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• 대한수학회논문집
• /
• 제24권3호
• /
• pp.321-331
• /
• 2009

In this paper, we investigate some fundamental properties and establish some results of f-derivations of BCI-algebras. Also, we prove Der(X), the collection of all f-derivations, form a semigroup under certain binary operation.

• Korean Journal of Mathematics
• /
• 제22권1호
• /
• pp.139-150
• /
• 2014

We introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras.

• 대한수학회논문집
• /
• 제26권1호
• /
• pp.13-21
• /
• 2011

The aim of this paper is to introduce the notion of permuting tri-f-derivations in lattices and to study some properties of permuting tri-f-derivations.

• East Asian mathematical journal
• /
• 제24권4호
• /
• pp.389-398
• /
• 2008

In this paper, some results of [6] concerning orthogonal ($\sigma$, $\tau$)-derivations and generalized ($\sigma$, $\tau$)-derivations are generalized for a nonzero ideal of a semiprime ring.