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Symmetric bi-derivations of subtraction algebras

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강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2021.06|한국수학논문집 (Korean Journal of Mathematics)|제29권 제2호|pp. 387-393

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키워드

derivationsymmetric bi-derivationSubtraction algebraisotone derivation
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초록

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map $D : X\times X\to X$ 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 $x, y, z\in X.$

Abstract

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map $D : X\times X\to X$ 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 $x, y, z\in X.$

참고문헌 (6)

  1. J. C. Abbott, "Sets, Lattices and Boolean Algebras" (1969), Allyn and Bacon
  2. S. D. Lee, "A note on multipliers of subtraction algebras", The Hacettepe Journal of Mathematics and Statistics, 42(2), pp.165~171 (2013)
  3. K. H. Kim, "A note on f-derivations of subtraction algebras", Scientiae Mathematicae Japonicae, 72(2), pp.127~132 (2010)
  4. B. M. Schein, "Difference Semigroups", Comm. in Algebra, 20, pp.2153~2169 (1992)
  5. Y. H. Yon, "On derivations of subtraction algebras", The Hacettepe Journal of Mathematics and statistics, 41(2), pp.157~168 (2012)
  6. B. Zelinka, "Subtraction Semigroups", Math. Bohemica, 120, pp.445~447 (1995)

관련 논문AI추천

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