- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 3
- Relative bi-ideals and relative quasi ideals in ordered semigroups
Relative bi-ideals and relative quasi ideals in ordered semigroups
Authors : Noor Mohammad Khan, Md. Firoj Ali
Pages : 950-961
Doi:10.15672/hujms.624046
View : 8 | Download : 2
Publication Date : 2020-06-02
Article Type : Research
Abstract :In this paper, after introducing the notion of relative bi-ideals and relative quasi ideals in ordered semigroups, some important properties of these bi-ideals and quasi ideals are studied. Then relatively prime and relatively weakly semiprime bi-ideals are defined and some vital results have been proved. We also define relative regularity and relative intra-regularity of an ordered semigroup and prove some results based on the connection among intra-regularity of an ordered semigroup, relative quasi and relative bi-ideals of that ordered semigroup. Finally some important results connecting relative regularity, relatively prime bi-ideals and relatively weakly semiprime bi-ideals of an ordered semigroup have also been obtained.Keywords : Ordered semigroups, ideals, relative ideals, bi-ideals, relative bi-ideals, relative quasi ideals, relatively prime and relatively weakly semiprime bi-ideals, relative regularity and relative intra-regularity