Relative Ideals in Ordered Semigroups

Md. Firoj Ali (), Noor Mohammad Khan () and Ahsan Mahboob ()
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Md. Firoj Ali: Aligarh Muslim University
Noor Mohammad Khan: Aligarh Muslim University
Ahsan Mahboob: Aligarh Muslim University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1497-1514

Abstract: Abstract In this paper, after introducing the notion of relative ideals in ordered semigroups, some important properties of these ideals are studied. Then notions of relatively prime and relatively weakly prime ideals are defined and some vital results have been proved. We also find some conditions under which relative ideals become left, right and two-sided ideals in any regular ordered semigroup. Finally, the notion of maximal and minimal relative ideals are introduced and some of their properties are studied.

Keywords: Ordered semigroups; ideals; relative ideals; relatively prime and relatively weakly prime ideals; maximal and minimal relative ideals; 06F05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0478-5

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