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2021•Indian Journal of Science and TechnologyOpen access

A Note on Full k-Ideals in Ternary Semirings

T Sunitha, U. Nagi Reddy, G. Shobhalatha

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Abstract

Objectives: k – ideals plays a vital role in ternary semirings. Ternary algebraic systems is a generalization of algebraic structures and it is the most natural way for the further development, deeper understanding of their properties. Methods: We have imposed Integral Multiple Property (IMP) and some other different constrains on a ternary semiring. Findings: In this study, we have described more results on the full k-ideal in the ternary semirings. Finally, we provide the characterization of full k-ideal in ternary semirings and studied their related properties. Applications: The structures of ideals in ternary semirings are widely applicable to computer sciences, dynamical and logical systems, cryptography, graph theory and artificial intelligence. Keywords Ternary Semiring, Ideal, k- Ideal, Full k- Ideal, Inverse

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Objectives: k – ideals plays a vital role in ternary semirings. Ternary algebraic systems is a generalization of algebraic structures and it is the most natural way for the further development, deeper understanding of their properties. Methods: We have imposed Integral Multiple Property (IMP) and some other different constrains on a ternary semiring. Findings: In this study, we have described more results on the full k-ideal in the ternary semirings. Finally, we provide the characterization of full k-ideal in ternary semirings and studied their related properties. Applications: The structures of ideals in ternary semirings are widely applicable to computer sciences, dynamical and logical systems, cryptography, graph theory and artificial intelligence. Keywords Ternary Semiring, Ideal, k- Ideal, Full k- Ideal, Inverse

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Available abstract

Objectives: k – ideals plays a vital role in ternary semirings. Ternary algebraic systems is a generalization of algebraic structures and it is the most natural way for the further development, deeper understanding of their properties. Methods: We have imposed Integral Multiple Property (IMP) and some other different constrains on a ternary semiring. Findings: In this study, we have described more results on the full k-ideal in the ternary semirings. Finally, we provide the characterization of full k-ideal in ternary semirings and studied their related properties. Applications: The structures of ideals in ternary semirings are widely applicable to computer sciences, dynamical and logical systems, cryptography, graph theory and artificial intelligence. Keywords Ternary Semiring, Ideal, k- Ideal, Full k- Ideal, Inverse

Key concepts: Semiring, Ternary operation, Ideal (ethics), Algebraic properties, Mathematics, Discrete mathematics, Generalization, Computer science

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