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On Partitioning and Subtractive Ideals of Ternary Semirings
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  • Journal title : Kyungpook mathematical journal
  • Volume 51, Issue 1,  2011, pp.69-76
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2011.51.1.069
 Title & Authors
On Partitioning and Subtractive Ideals of Ternary Semirings
Chaudhari, Jaiprakash Ninu; Ingale, Kunal Julal;
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In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/ is essentially independent of choice of Q. 2) If f : S S' is a maximal ternary semiring homomorphism, then S/ker S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I A if and only if A/ = {q + I : q Q A} is a subtractive idea of S/.
Ternary semiring;subtractive ideal;partitioning ideal;quotient ternary semiring;maximal homomorphism;isomorphism;
 Cited by
On Partitioning and Subtractive Ideals of Ternary Semirings,Chaudhari, Jaiprakash Ninu;Ingale, Kunal Julal;

Kyungpook mathematical journal, 2011. vol.51. 1, pp.69-76 crossref(new window)
Paul J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21(1969), 412-416. crossref(new window)

Paul J. Allen, J. Neggers and H. S. Kim, Ideal theory in commutative A-semirings, Kyungpook, Math. Journal, 46(2006), 261-271.

Shahabaddin Ebrahimi Atani, The ideal theory in quotient of commutative semirings, Glasnik Matematicki, 42(62)(2007), 301-308. crossref(new window)

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

T. K. Dutta and S. Kar, On The Jacobson Radical of A Ternary Semiring, Southeast Asian Bulletin of Mathematics, 28(1)(2004), 1-13.

T. K. Dutta and S. Kar, On Prime Ideals And Prime Radical of Ternary Semirings, Bull. Cal. Math. Soc., 97(5)(2005), 445-454.

T. K. Dutta and S. Kar, A Note on Regular Ternary Semirings, Kyungpook Math. J., 46(2006), 357-365.

J. S. Golan, Semiring and their Applications, Kluwer Academic publisher Dordrecht, 1999.

Vishnu Gupta and J. N. Chaudhari, On Right ${\pi}$-Regular Semirings, Sarajevo Journal of Mathematics, 2(14)(2006), 3-9.

Vishnu Gupta and J. N. Chaudhari, On Partitioning ideals of Semirings, Kyungpook Math. Journal, 46(2006), 181-184.

S. Kar, Ideal Theory in the Ternary Semiring $\mathbb{Z}^{-}_{0}$, Bull. Malaysian. Math. Sci. Soc., (2), to appear.

D. H. Lehmer, A ternary analogue of abelian groups, American Journal of Mathematics, 59(1932), 329-338.