Abstract. The purpose of this paper is to introduce the notion of derivation, differential ideal, differential k-ideal (differential h-ideal) in ternary semiring and to study the validity of some of the results on prime ideals and prime radicals of ternary semirings replacing ideals by differential ideals, radicals by differential radicals, ternary semirings by differential ternary semirings.Among others we deduce that a radical differential ideal I in a differential ternary semiring is the intersection of all prime differential ideals containing I. Also we deduce that in a differential ternary semiring satisfying ascending chain condition on radical differential ideals any radical differential ideal is expressible as the intersection of finite number of differential ideals.

Received: June 14, 2016

Revised: July 28, 2016

Published: October 9, 2016

AMS Subject Classification: 16Y60, 16Y30

Key Words and Phrases: ternary semiring, differential ternary semiring, differential ideal, differential k-ideal, differential h-ideal, radical differential ideal, radical differential k-ideal, radical differential h-ideal
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Bibliography

1

T.K. Dutta, S. Kar, On regular ternary semiring, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific (2003), 343-355.

2

T.K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Cal. Math. Soc., 97, No. 5 (2005), 445-454.

3

T.K. Dutta and S. Kar, On semiprime ideals and irreducible ideals of ternary semirings, Bull. Cal. Math. Soc., 97, No. 5 (2005), 467-476.

4

T.K. Dutta, S Mandal, J. Sircar, On uniformly strongly prime ternary semiring, South East asian Bulletin Mathematics, 63 (2012), 43-56.

5

W. G. Lister, Ternary rings, Trans. Amer. Soc., 154 (1971), 37-55.

6

Merry Sultana, Sujit Kumar Sardar, Jayasri Sircar, Prime radical and radical ideal in ternary semiring, International Journal of Pure and Applied Mathematics, 108, No. 3 (2016), 523-531, doi: 10.12732/ijpam.v108i3.5.

7

Sujit Kumar Sardar and Sarbani Goswami, On derivation in semirings, Southeast Asian Bulletin of Mathematics, 33 (2009), 917-928.

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DOI: 10.12732/ijpam.v109i4.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 779 - 788

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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