Korean J. Math.  Vol 29, No 2 (2021)  pp.387-393
DOI: https://doi.org/10.11568/kjm.2021.29.2.387

Symmetric bi-derivations of subtraction algebras

Kyung Ho Kim

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 $x, y, z\in X.$

Keywords


Subtraction algebra, derivation, symmetric bi-derivation, isotone derivation.

Subject classification

16Y99; 20N20

Sponsor(s)



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References


J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston 1969. (Google Scholar)

S. D. Lee and K. H. Kim, A note on multipliers of subtraction algebras, The Hacettepe Journal of Mathematics and Statistics, 42 (2) (2013), 165–171. (Google Scholar)

K. H. Kim, A note on f-derivations of subtraction algebras, Scientiae Mathematicae Japonicae, 72 (2) (2010), 127–132. (Google Scholar)

B. M. Schein, Difference Semigroups, Comm. in Algebra 20 (1992), 2153–2169. (Google Scholar)

Y. H. Yon and K. H. Kim, On derivations of subtraction algebras, The Hacettepe Journal of Mathematics and Statistics, 41 (2) (2012), 157–168 (Google Scholar)

B. Zelinka, Subtraction Semigroups, Math. Bohemica, 120 (1995), 445–447. (Google Scholar)


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