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3-Absorbing Principal T-Ideals in the Ternary Semiring of Non-positive Integers


Affiliations
1 Department of Mathematics, M. J. College, Jalgaon, India
     

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Since the product of even number of elements of ternary semiring S may not be element of S, the concept of 2-absorbing ideal in S can not be defined. In this paper, we introduce the concept of 3-absorbing ideals in a commutative ternary semiring with identity element and obtain characterizations of 3-absorbing principal ideals and 3-absorbing principal T-ideals in the ternary semiring of non-positive integers.

Keywords

Ternary Semiring, Prime Ideal, 3-absorbing Ideal, Finitely Generated Ideal, T-ideal.
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  • Ayman Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. Vol. 75(2007), 417āˆ’429.

  • J. N. Chaudhari, 2-absorbing ideals in semirings, International Journal of Algebra 6(6)(2012), 265-270.

  • J. N. Chaudhari, 2-absorbing ideals in the semiring of non-negative integers, Journal of the Indian Math. Soc. 80(2013), no. 3-4, 235-241.

  • J. N. Chaudhari and K. J. Ingale, A note on ideals in the semiring Z+0, Journal of the Indian Math. Soc. 79(2012), no. 1-4, 33-39.

  • J. N. Chaudhari and K. J. Ingale, Ideals in the ternary semiring of non-positve integers, Bull. Malaysian Math. Sci. Soc. (2) 37(4) (2014), 1149-1156.

  • 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 prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97(2005), no. 5, 445-454.

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

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

  • V. Gupta and J. N. Chaudhari, Prime ideals in semirings, Bull. Malaysian Math. Sci. Soc., (2)34(2)(2011), 417-421.

  • S. Kar, Ideal theory in the ternary semiring Zāˆ’0, Bull. Malaysian Math. Sci. Soc .(2)34(2011), no. 1, 69-77.

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


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  • 3-Absorbing Principal T-Ideals in the Ternary Semiring of Non-positive Integers

Abstract Views: 551  |  PDF Views: 1

Authors

K. J. Ingale
Department of Mathematics, M. J. College, Jalgaon, India
J. N. Chaudhari
Department of Mathematics, M. J. College, Jalgaon, India

Abstract


Since the product of even number of elements of ternary semiring S may not be element of S, the concept of 2-absorbing ideal in S can not be defined. In this paper, we introduce the concept of 3-absorbing ideals in a commutative ternary semiring with identity element and obtain characterizations of 3-absorbing principal ideals and 3-absorbing principal T-ideals in the ternary semiring of non-positive integers.

Keywords


Ternary Semiring, Prime Ideal, 3-absorbing Ideal, Finitely Generated Ideal, T-ideal.

References