The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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MODULE LEFT (m, n)-DERIVATIONS

  • Cui, Yinhua (Department of Mathematics, Yanbian University) ;
  • Shin, Dong Yun (Department of Mathematics, University of Seoul)
  • Received : 2016.11.08
  • Accepted : 2017.02.03
  • Published : 2017.02.28
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Abstract

$Fo{\check{s}}ner$ [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 $m{\neq}n$.

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References

  1. A. Fosner: On the generalized Hyers-Ulam stability of module left (m; n)-derivations. Aequationes. Math. 84 (2012), 91-98. https://doi.org/10.1007/s00010-012-0124-3
  2. Y. Jung: On the generalized Hyers-Ulam stability of module left derivations. J. Math. Anal. Appl. 339 (2008), 108-114. https://doi.org/10.1016/j.jmaa.2007.07.003