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Abbasi, Mohammad Yahya
- An Introduction of Theory of Involutions in Ordered Semihypergroups and their Weakly Prime Hyperideals
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Authors
Affiliations
1 Department of Mathematics, Jamia Millia Islamia, New Delhi - 110 025, IN
1 Department of Mathematics, Jamia Millia Islamia, New Delhi - 110 025, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 3-4 (2019), Pagination: 230-240Abstract
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.Keywords
Semigroup, Ordered Semihypergroup, Hyperideal, Involution, Weakly Prime Hyperideal.
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