On right chain ordered semihypergroups

Volume 24, Issue 1, pp 59--72 http://dx.doi.org/10.22436/jmcs.024.01.06

Publication Date: December 24, 2020 Submission Date: October 29, 2020 Revision Date: November 25, 2020 Accteptance Date: December 02, 2020

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Authors

Pairote Yiarayong - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. Bijan Davvaz - Department of Mathematics , Yazd University, Yazd, Iran. Ronnason Chinram - Division of Computational Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand.

Abstract

The purposes of this paper are to introduce generalizations of the right chain ordered semigroups to the context of the right chain ordered semihypergroups. Furthermore, we present the concepts of prime, completely prime, semiprime, and completely semiprime right hyperideals of ordered semihypergroups. We also introduce the idea of associated prime right hyperideals. Moreover, we give some characterizations of prime, completely prime, semiprime, and completely semiprime right hyperideals of ordered semihypergroups. Finally, we obtain necessary and sufficient prime right hyperideal conditions to be a semiprime right hyperideal.

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Keywords

• Ordered semihypergroup
• prime right hyperideal
• completely prime right hyperideal
• semiprime right hyperideal
• completely semiprime right hyperideal

MSC

•  20N20
•  06F05

References

• [1] T. Changphas, B. Davvaz, Properties of hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math., 33 (2014), 425--432
  • View Article
  • MathSciNet


• [2] T. Changphas, P. Luangchaisri, R. Mazurek, On right chain ordered semigroups, Semigroup Forum, 96 (2018), 523--535
  • View Article
  • MathSciNet


• [3] B. Davvaz, P. Corsini, T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseudoorder, European J. Combin., 44 (2015), 208--217
  • View Article
  • MathSciNet


• [4] M. Farooq, A. Khan, B. Davvaz, Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals, Soft Comput, 22 (2018), 3001--3010
  • View Article
  • Google Scholar


• [5] M. Ferrero, R. Mazurek, A. Sant’Ana, On right chain semigroups, J. Algebra, 292 (2005), 574--584
  • View Article
  • MathSciNet


• [6] S. H. Ghazavi, S. M. Anvariyeh, S. Mirvakili, $EL^2$–hyperstructures Derived from (Partially) Quasi Ordered Hyperstructures, Iran. J. Math. Sci. Inform., 10 (2015), 99--114
  • View Article
  • Google Scholar


• [7] Z. Gu, X. Tang, Ordered regular equivalence relations on ordered semihypergroups, J. Algebra, 450 (2016), 384--397
  • View Article
  • MathSciNet


• [8] Z. Gu, X.Tang, Characterizations of (strongly) ordered regular relations on ordered semihypergroups, J. Algebra, 465 (2016), 100--110
  • View Article
  • MathSciNet


• [9] D. Heidari, B. Davvaz, On ordered hyperstructures, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 73 (2011), 85--96
  • View Article
  • MathSciNet


• [10] S. Omidi, B. Davvaz, Contribution to study special kinds of hyperideals in ordered semihyperrings, J. Taibah Univ. Sci., 11 (2017), 1083--1094
  • View Article
  • Google Scholar


• [11] S. Omidi, B. Davvaz, J .M. Zhan, An investigation on ordered algebraic hyperstructures, Acta Math. Sin. (Engl. Ser.), 33 (2017), 1107--1124
  • View Article
  • Google Scholar


• [12] J. Tang, B. Davvaz, Y. Luo, Hyperfilters and fuzzy hyperfilters of ordered semihypergroups, J. Intell. Fuzzy Systems, 29 (2015), 75--84
  • View Article
  • MathSciNet


• [13] J. Tang, B. Davvaz, X.-Y. Xie, An investigation on hyper S-posets over ordered semihypergroups, Open Math., 15 (2017), 37--56
  • View Article
  • MathSciNet


• [14] J. Tang, Y. Luo, X. Xie, A study on (strong) order-congruences in ordered semihypergroups, Turk. J. Math., 42 (2018), 1255--1271
  • View Article
  • MathSciNet


• [15] J. Tang, X. Xie, An investigation on left hyperideals of ordered semihypergroups, J. Math. Res. Appl., 37 (2017), 419--434
  • View Article
  • MathSciNet