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Volume-1 Issue-4, February 2015, ISSN: 2394-367X (Online)
Published By: Blue Eyes Intelligence Engineering & Sciences Publication Pvt. Ltd. 

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1.

Authors:

D. Madhusudhana Rao, G. Srinivasa Rao

Paper Title:

Prime Radicals and Completely Prime Radicals in Ternary Semirings

Abstract: In this paper we introduced prime radicals and completely prime radicals in ternary smearing. It is proved that : If A, B and C are any three ideals of a ternary semiring T, then i) A  B  A  B , ii) if A ∩ B∩ C ≠ ∅ then ABC  ABC  A  B  C iii) A = A . Further it is proved that an ideal Q of ternary semiring T is a semiprime ideal of T if and only if Q =Q. It is proved that if P is a prime ideal of a ternary semiring T, then ( )n P = P for all odd natural numbers nN and if A is an ideal of a ternary semiring T then A ={x ∈ T: every msystem of T containing x meets A} i.e., A = { xT :M(x) A }. Mathematical Subject Classification: 16Y30, 16Y99.

Keywords: left simple, lateral simple, right simple, simple, duo ternary semiring,semisimple ternary semiring, globally idempotent.

References:
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2.       Dixit, V.N. and Dewan, S., A note on quasi and bi-ideals in ternary semigroups,  Int. J. Math. Math. Sci. 18, no. 3(1995),  501{508.

3.     Dutta, T.K. and Kar, S., On regular ternary semirings,  Advances in Algebra Proceedings of the ICM Satellite Conference  in Algebra and Related Topics, World Scienti¯c, New Jersey, 2003, 3IV3{355.

4.       Dheena. P, Manvisan. S., P-prime and small P-prime ideals in semirings, International Journal of Algebra and Statistics, Volume 1; 2(2012), 89-93.

5.       Dutta, T.K. and Kar, S., A note on regular ternary semirings, Kyung-pook Math. J., IV6 (2006), 357{365.

6.       Kar, S., On quasi-ideals and bi- ideals in ternary semirings, Int. J. Math.Math.Sc., 18 (2005), 3015{3023.

7.       Lehmer. D. H., A ternary analogue of abelian groups, Amer.  J. Math., 59(1932),  329-338.

8.       Lister, W.G., Ternary rings, Trans Amer.  Math.Soc., 15IV  (1971), 37- 55.

9.       MadhusudhanaRao. D., Primary Ideals in Quasi-Commutative Ternary Semigroups International Research Journal of Pure Algebra – 3(7), 2013, 25IV-258.

10.     Madhusduhana Rao. D. and Srinivasa Rao. G., A Study on Ternary Semirings, International Journal of Mathematical Archive-5(12), Dec.-2014, 24-30.

11.     MadhusudhanaRao. D. and SrinivasaRao. G., Special Elements of a Ternary Semirings, International Journal of Engineering Research and Applications, Vol. IV, Issue 1(Version-5), November 201IV, pp. 123-130.

12.     MadhusudhanaRao. D. and SrinivasaRao. G., Concepts on Ternary Semirings, International Journal of Modern Science and Engineering Technology, Volume 1, Issue 7, 201IV, pp. 105-110. 

13.     MadhusudhanaRao. D. and SrinivasaRao. G., Characteristics of Ternary Semirings, International Journal of Engineering Research and Management – Vol.2, Issue 01, January 2015, pp. 3-6.

14.  MadhusudhanaRao. D. and SrinivasaRao. G.,Structure of Certain Ideals in Ternary Semirings-International Journal of Innovative Science and Modern Engineering(IJISME)-Volume-3, Issue-2, January, 2015.

 

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