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


Affiliations

  • M. J. College, Department of Mathematics, Jalgaon, 425002, 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.

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References

Ayman Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. Vol. 75(2007), 417−429.

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 Z0, 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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