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On Minimal and Maximal Hyperidealsin n -ary Semihypergroups

Author

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  • Jukkrit Daengsaen

    (PhD Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Sorasak Leeratanavalee

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Bijan Davvaz

    (Department of Mathematics, Yazd University, Yazd 89139, Iran)

Abstract

The concept of j -hyperideals, for all positive integers 1 ≤ j ≤ n and n ≥ 2 , in n -ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first introduce the concept of j -(0-)simple n -ary semihypergroups and discuss their related properties through terms of j -hyperideals. Furthermore, we characterize the minimality and maximality of j -hyperideals in n -ary semihypergroups and establish the relationships between the (0-)minimal, maximal j -hyperideals and the j -(0-)simple n -ary semihypergroups. Our main results are to extend and generalize the results on semihypergroups and ternary semihypergroups. Moreover, a related question raised by Petchkaew and Chinram is solved.

Suggested Citation

  • Jukkrit Daengsaen & Sorasak Leeratanavalee & Bijan Davvaz, 2020. "On Minimal and Maximal Hyperidealsin n -ary Semihypergroups," Mathematics, MDPI, vol. 8(10), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1656-:d:419630
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    References listed on IDEAS

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    1. V. N. Dixit & Sarita Dewan, 1995. "A note on Quasi and Bi-ideals in Ternary semigroups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 18, pages 1-8, January.
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    Cited by:

    1. Jukkrit Daengsaen & Sorasak Leeratanavalee, 2021. "Regularities in Ordered n -Ary Semihypergroups," Mathematics, MDPI, vol. 9(16), pages 1-21, August.

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