Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATIONS OF ORDERED INTRA k-REGULAR SEMIRINGS BY ORDERED k-IDEALS

  • Received : 2016.12.21
  • Accepted : 2017.11.21
  • Published : 2018.01.31
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Abstract

We introduce the notion of ordered intra k-regular semirings, characterize them using their ordered k-ideals and prove that an ordered semiring S is both ordered k-regular and ordered intra k-regular if and only if every ordered quasi k-ideal or every ordered k-bi-ideal of S is ordered k-idempotent.

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References

  1. M. R. Adhikari, M. K. Sen, and H. J. Weinert, On k-regular semirings, Bull. Calcutta Math. Soc. 88 (1996), no. 2, 141-144.
  2. J. Ahsan, J. N. Mordeson, and M. Shabir, Fuzzy semirings with applications to automata theory, Studies in Fuzziness and Soft Computing, 278, Springer, Heidelberg, 2012.
  3. A. K. Bhuniya and K. Jana, Bi-ideals in k-regular and intra k-regular semirings, Discuss. Math. Gen. Algebra Appl. 31 (2011), no. 1, 5-25. https://doi.org/10.7151/dmgaa.1172
  4. S. Bourne, The Jacobson radical of a semiring, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), no. 3, 163-170. https://doi.org/10.1073/pnas.37.3.163
  5. A. P. Gan and Y. L. Jiang, On ordered ideals in ordered semirings, J. Math. Res. Exposition 31 (2011), no. 6, 989-996.
  6. K. Jana, Quasi k-ideals in k-regular and intra k-regular semirings, Pure Math. Appl. (PU.M.A.) 22 (2011), no. 1, 65-74.
  7. S. Lajos, A note on intra-regular semigroups, Proc. Japan Acad. 39 (1963), 626-627.
  8. D. Mandal, Fuzzy ideals and fuzzy interior ideals in ordered semirings, Fuzzy Inf. Eng. 6 (2014), no. 1, 101-114. https://doi.org/10.1016/j.fiae.2014.06.008
  9. P. Palakawong na Ayutthaya and B. Pibaljommee, Characterizations of regular ordered semirings by ordered quasi-ideals, Int. J. Math. Math. Sci. 2016, Art. ID 4272451, 8 pp.
  10. P. Palakawong na Ayutthaya and B. Pibaljommee, Characterizations of intra-regular ordered semirings by ordered quasi-ideals, Proceeding of The National and International Graduate Research Conference, Graduate School, Khon Kaen University, Thailand, (2016), 102-109.
  11. P. Palakawong na Ayutthaya and B. Pibaljommee, Characterizations of ordered k-regular semirings by ordered quasi k-ideals, Quasigroups Related Systems 25 (2017), no. 1, 109-120.
  12. S. Patchakhieo and B. Pibaljommee, Characterizations of ordered k-regular semirings by ordered k-ideals, Asian-Eur. J. Math. 10 (2017), no. 2, 1750020, 14 pp. https://doi.org/10.1142/S1793557117500206
  13. P. Senarat and B. Pibaljommee, Prime ordered k-bi-ideals in ordered semirings, Quasi-groups Related Systems 25 (2017), no. 1, 121-132.
  14. M. Shabir, A. Ali, and S. Batool, A note on quasi-ideals in semirings, Southeast Asian Bull. Math. 27 (2004), no. 5, 923-928.