An Excursion Through Some Characterizations of Hypersemigroups By Normal Hyperideals

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2019 by IJMTT Journal
Volume-65 Issue-12
Year of Publication : 2019
Authors : Abul Basar, Shahnawaz Ali, Poonam Kumar sharma
  10.14445/22315373/IJMTT-V65I12P515

MLA

MLA Style:Abul Basar, Shahnawaz Ali, Poonam Kumar sharma "An Excursion Through Some Characterizations of Hypersemigroups By Normal Hyperideals" International Journal of Mathematics Trends and Technology 65.12 (2019):142-147. 

APA Style: Abul Basar, Shahnawaz Ali, Poonam Kumar sharma(2019). An Excursion Through Some Characterizations of Hypersemigroups By Normal Hyperideals International Journal of Mathematics Trends and Technology, 142-147.

Abstract
In this paper, we introduce normal hyperideal and bi-hyperideal in normal hypersemigroups. We study (normal)hypersemigroup and normal regular hypersemigroup based on bi-hyperideal proving some equivalent conditions. In particular, we prove, among the other results, that if I1,Iare any two normal hyperideals of a hypersemigroup H, then their product I1 • I2 and I2  • I1 are also normal hyperideals of S and I1 • I2 = I2 • I1. We also prove that the minimal normal hyperideal of hypersemigroup H is a hypergroup.

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Keywords
hypersemigroup, bihyperideal, normal hyperideal, bi-hyperideal