• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권4호
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• pp.385-387
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• 2016

$Fo{\check{s}}ner$ [4] defined a generalized module left (m, n)-derivation and proved the Hyers-Ulam stability of generalized module left (m, n)-derivations. In this note, we prove that every generalized module left (m, n)-derivation is trival if the algebra is unital and $m{\neq}n$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권1호
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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 $m{\neq}n$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권1호
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• pp.99-106
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• 2009

In this paper, we improve the generalized Hyers-Ulam stability and the superstability of module left derivations due to the results of [7].

• 대한수학회보
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• 제33권2호
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• pp.221-228
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• 1996

Throughout, R will represent an associative ring with center Z(R). A module X is said to be n-torsionfree, where n is an integer, if nx = 0, $x \in X$ implies x = 0. An additive mapping $D : R \to X$, where X is a left R-module, will be called a Jordan left derivation if $D(a^2) = 2aD(a), a \in R$. M. Bresar and J. Vukman [1] showed that the existence of a nonzero Jordan left derivation of R into X implies R is commutative if X is a 2-torsionfree and 3-torsionfree left R-module.