Korean J. Math. Vol. 27 No. 3 (2019) pp.779-791
DOI: https://doi.org/10.11568/kjm.2019.27.3.779

A note on derivations of ordered $\Gamma$-semirings

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Published: Sep 30, 2019
Keywords:
Semiring, ordered Gamma-semiring, reverse derivation, positively ordered, idempotent
Mathematics Subject Classification:
16Y30, 06B35, 06B99

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KyungHo Kim
Department of Mathematics Korea National University of Transportation Chungju 27469, Korea

Abstract

In this paper, we consider derivation of an ordered $\Gamma$-semiring and introduce the notion of reverse derivation on ordered $\Gamma$-semiring. Also, we obtain some interesting related properties. Let $I$ be a nonzero ideal of prime ordered $\Gamma$-semiring $M$ and let $d$ be a nonzero derivation of $M.$ If $\Gamma$-semiring $M$ is negatively ordered, then $d$ is nonzero on $I.$


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References

[1] M. Bresar and J. Vuckman, On the left derivations and related mappings, Proc. Math Soc 10 (1990), 7–16 Google Scholar

[2] K. H. Kim On right derivations of incline algebras, J. Chungcheong Math Soc 26 (2013), 683–690. Google Scholar

[3] K. H. Kim, On generalized right derivations of incline algebras, Gulf J. Math 3 (2015), 127–132. Google Scholar

[4] M. Murali Krishna Rao, Γ-semiring-I, Southeast Asian Bull Math 19 (1995), 45–54. Google Scholar

[5] M. Murali Krishna Rao, Γ-semiring-II, Southeast Asian Bull Math 21 (1997), 45–54. Google Scholar

[6] M. Murali Krishna Rao, Right derivation of ordered Γ-semirings, Dicussiones Mathematicea, General Algebra and Application 36 (2016), 209–221. Google Scholar

[7] N. Nobusawa, On generalization of the ring theory, Osaka J. Math 1 (1964), 81–89. Google Scholar

[8] E. C. Posner, Derivations in prime rings, Proc. Math Soc 8 (1957), 1093–1100. Google Scholar

[9] M. K. Sen, On Γ-semigroup, Proc. of International Conference of algebraic its Applications, Decker Publication (Ed(s)), New York, 1981, 301–308. Google Scholar

[10] H. S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math 40 (1934), 14–21. Google Scholar