The Journal of the Indian Mathematical Society

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

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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