DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

N. Sarasit

Napaporn Sarasit

Division of Mathematics
Faculty of Engineering, Rajamangala University of Technology Isan
Khon Kaen Campus, Khon Kaen 40000, Thailand

email: napaporn.sr@rmuti.ac.th

R. Chinram

Ronnason Chinram

Division of Computational Science
Faculty of Science, Prince of Songkla University
Hat Yai, Songkhla 90110, Thailand

email: ronnason.c@psu.ac.th

Title:

$(f,g)$-derivation of ordered ternary semirings

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Source:

Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 149-159

Received: 2021-07-07 , Revised: 2021-08-04 , Accepted: 2022-05-04 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1413

Abstract:

In this paper, we introduce the concept of an $(f, g)$-derivation of ternary semirings and we study its properties in ordered ternary semirings. We prove that if $d$ is an $(f, g)$-derivation of an ordered ternary semiring $S$, then the kernel of $d$ is a $k$-ideal of $S$. Moreover, we show that the kernel and the set of all fixed points of $d$ are $m$-$k$-ideals of $S$.

Keywords:

ordered ternary semiring, derivation, integral ordered ternary semiring

References:

  1. M. Bresar and J. Vukman, On the left derivation and related mappings, Proc. Amer. Math. Soc 110 (1990) 7–16.
  2. T.K. Dutta and S. Kar, On regular ternary semirings, in: Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics (Ed(s)), (World Scientific, New Jersey 2003) 343–355.
  3. E. Kasner, An extension of the group concept (reported by L.G. Weld), Bull. Amer. Math. Soc. 10 (1904) 290–291.
  4. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 59 (1932) 329–388.
  5. W. G. Lister, Ternary rings, Tran. of Amer. Math. Soc. 154 (1971) 37–55.
  6. M. Murali Krishna Rao and B. Venkateswarlu, Right derivation of ordered $Γ$-semirings, Discuss. Math. Gen. Algebra Appl. 36 (2016) 209–221.
  7. M. Murali Krishna Rao, On $Γ$-semiring with identity, Discuss. Math. Gen. Algebra Appl. 37 (2017) 189–207.
  8. M. Murali Krishna Rao, Ideals in ordered $Γ$-semirings, Discuss. Math. Gen. Algebra Appl. 38 (2018) 47–68.
  9. M. Murali Krishna Rao, $(f,g)$-derivation of ordered semirings, Analele Universităţii Oradea Fasc. Matematica 26 (2) (2019) 41–49.
  10. H. Prüfer, Thorie der Abelschen Gruppen, Mathematische Zeitschrift 20 (1924) 165–187.
  11. H. S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. (N.S.) 40 (1934) 914–920.
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