A Generalization of m-Bi-Ideals in b-Semirings and Its Characterizing Extension

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DOI: https://doi.org/10.28924/2291-8639-22-2024-89
Published: May 27, 2024
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M. Suguna, K. Saranya, Aiyared Iampan, A Generalization of m-Bi-Ideals in b-Semirings and Its Characterizing Extension, Int. J. Anal. Appl., 22 (2024), 89.

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M. Suguna, K. Saranya, Aiyared Iampan

Abstract

In this study, we introduce new types of m-quasi-ideals and m-bi-ideals in b-semirings and provide some characterizations of these ideals. We use an algebraic method to express the fundamental properties of m-bi-ideals in b-semirings. We also discuss the m-ideals in terms of their algebraic structures. Moreover, we examine the m-bi-ideals and their generators and provide some characterizations regarding bi-ideals. We further discuss the m-bi-ideal generated by a non-empty subset S, which is denoted by <S>m= S∪Σfinite BSmB, where B is the set of all bi-ideals.

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References

  1. R. Chinram, An Introduction to b-Semirings, Int. J. Contemp. Math. Sci. 4 (2009), 649–657.
  2. R. Chinram, A Note on (m, n)-Quasi-Ideals in Semirings, Int. J. Pure Appl. Math. 49 (2008), 45–52.
  3. J.S. Golan, Theory of Semirings with Applications in Mathematics and Theoretical Computer Science, AddisonWesley Longman Ltd., Harlow, 1992.
  4. J.M. Howie, Introduction to Semigroup Theory, Academic Press, 1976.
  5. K. Iséki, Quasiideals in Semirings Without Zero, Proc. Japan Acad. Ser. A Math. Sci. 34 (1958), 79–81. https://doi.org/10.3792/pja/1195524783.
  6. S. Kar, B. Maity, Some Ideals of Ternary Semigroups, Ann. Alex. Ioan Cuza Univ. - Math. 57 (2011), 247–258. https://doi.org/10.2478/v10157-011-0024-1.
  7. S. Lajos, F.A. Szász, On the Bi-Ideals in Associative Rings, Proc. Japan Acad. Ser. A Math. Sci. 46 (1970), 505–507. https://doi.org/10.3792/pja/1195520265.
  8. G. Mohanraj and M. Palanikumar, Characterization of Regular b-Semirings, Math. Sci. Int. Res. J. 7 (2018), 117–123.
  9. M. Munir, M. Habib, Characterizing Semirings using Their Quasi and Bi-Ideals, Proc. Pak. Acad. Sci.: A. Phys. Comput. Sci. 53 (2016), 469–475.
  10. M. Palanikumar, K. Arulmozhi, On Various Almost Ideals of Semirings, Ann. Commun. Math. 4 (2021), 17–25. https://doi.org/10.5281/zenodo.10048905.
  11. M. Palanikumar, K. Arulmozhi, C. Jana, M. Pal, K.P. Shum, New Approach Towards Different Bi-Base of Ordered b-Semiring, Asian-Eur. J. Math. 16 (2022), 2350019. https://doi.org/10.1142/s1793557123500195.
  12. O. Steinfeld, Quasi-Ideals in Rings and Semigroups, Akadémiai Kiadó, Budapest, 1978.
  13. O. Steinfeld, Über die Quasiideale von Halbgruppen, Publ. Math. Debrecen. 4 (2022), 262–275. https://cir.nii.ac.jp/crid/1360016866456979456.
  14. M. Suguna, M. Palanikumar, A. Iampan, M. Geethalakshmi, New Approach towards Different Types of Bi-Quasi Ideals in b-Semirings and Its Extension, Int. J. Innov. Comput. Inf. Control. 20 (2024), 75–87. https://doi.org/10.24507/ijicic.20.01.75.
  15. H.S. Vandiver, Note on a Simple Type of Algebra in Which the Cancellation Law of Addition Does Not Hold, Bull. Amer. Math. Soc. 40 (1934), 914–920. https://doi.org/10.1090/s0002-9904-1934-06003-8.