An Introduction of Theory of Involutions in Ordered Semihypergroups and their Weakly Prime Hyperideals

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Authors

  • Abul Basar
     Department of Mathematics, Jamia Millia Islamia, New Delhi - 110 025 ,IN
  • Mohammad Yahya Abbasi
     Department of Mathematics, Jamia Millia Islamia, New Delhi - 110 025 ,IN
  • Sabahat Ali Khan
     Department of Mathematics, Jamia Millia Islamia, New Delhi - 110 025 ,IN

DOI:

https://doi.org/10.18311/jims/2019/23401

Keywords:

semigroup, ordered semihypergroup, hyperideal, involution, weakly prime hyperideal

Abstract

In this paper, we introduce ordered semihypergroups with involution and weakly prime semihyperideal, then we investigate some properties of prime, semiprime and weakly prime hyperideals in ordered semihypergroup with involution. Also, we study intra-regular ordered semihypergroups with involution. We prove that in ordered semihypergroup S with involution such that the involution preserves the order, a semihyperideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime hyperideals of S coincide. Finally, we show that if S is an ordered semi- hypergroup with order preserving involution, then the semihyperideals of S are prime if and only if it is intra-regular.

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Published

2019-08-22

How to Cite

Basar, A., Yahya Abbasi, M., & Ali Khan, S. (2019). An Introduction of Theory of Involutions in Ordered Semihypergroups and their Weakly Prime Hyperideals. The Journal of the Indian Mathematical Society, 86(3-4), 230–240. https://doi.org/10.18311/jims/2019/23401

Issue

Volume 86, Issue 3-4, July-December 2019

Section

Articles

License

Copyright (c) 2019 Abul Basar, Mohammad Yahya Abbasi, Sabahat Ali Khan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2019-03-12
Accepted 2019-03-20
Published 2019-08-22

 

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