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

KyungHo Kim

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 $I.$

Keywords


Semiring, ordered Gamma-semiring, reverse derivation, positively ordered, idempotent

Subject classification

16Y30, 06B35, 06B99

Sponsor(s)



Full Text:

PDF

References


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

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

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

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

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

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

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

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

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)

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)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr