Different Partial Prime Bi-Ideals and Its Extension of Partial Ternary Semirings

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DOI: https://doi.org/10.28924/2291-8639-22-2024-145
Published: Aug 20, 2024
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M. Palanikumar, V. Nagarani, M.H.A. Aysha Chithukka, Aiyared Iampan, M.S. Malchijah Raj, Different Partial Prime Bi-Ideals and Its Extension of Partial Ternary Semirings, Int. J. Anal. Appl., 22 (2024), 145.

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M. Palanikumar, V. Nagarani, M.H.A. Aysha Chithukka, Aiyared Iampan, M.S. Malchijah Raj

Abstract

We discuss the partial bi-ideal of partial ternary semirings S. The partial bi-ideal is a new generalization of the ideal. To determine the relationships between the three types of partial prime bi-ideals and their examples. We constructed the partial right ideal, partial lateral ideal, partial left ideal, partial ideal, and partial bi-ideal generated by a single element. We interact with the relationships between HQ, LQ and RQ, where Q is bi-ideal. Consequently, we defined three distinct partial m-systems. The partial bi-ideal P of S is a partial 2-prime if and only if Z1Z2Z3⊆P, where Z1 is a partial right ideal, Z2 is a partial lateral ideal and Z3 is a partial left ideal of S implies either one of Z1⊆P, Z2⊆P and Z3⊆P. Also, we discuss HQ is a unique biggest two-sided partial prime ideal of S contained Q. Suppose that M is a partial m3-system and partial bi-ideal Q of S with Q∩M is empty, there exists a partial 3-prime P of S containing Q which includes P∩M=∅. Finally, examples were provided to illustrate the results.

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