$(m,n)$-Hyperideals in Ordered Semihypergroups

Mahboob, Ahsan; Khan, Noor Mohammad; Davvaz, Bijan

doi:10.29252/cgasa.12.1.43

	$(m,n)$-Hyperideals in Ordered Semihypergroups
Categories and General Algebraic Structures with Applications
مقاله 4، دوره 12، شماره 1، فروردین 2020، صفحه 43-67 اصل مقاله (659.07 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.29252/cgasa.12.1.43
نویسندگان
Ahsan Mahboob¹؛ Noor Mohammad Khan¹؛ Bijan Davvaz²
¹Aligarh Muslim University
²Yazd University
چکیده
In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideals, respectively. The relations ${_m\mathcal{I}}, \mathcal{I}_n, \mathcal{H}_m^n$, and $\mathcal{B}_m^n$ on an ordered semihypergroup are, then, introduced. We prove that $\mathcal{B}_m^n \subseteq \mathcal{H}_m^n$ on an ordered semihypergroup and provide a condition under which equality holds in the above inclusion. We also show that the $(m,0)$-regularity [$(0,n)$-regularity] of an element induce the $(m,0)$-regularity [$(0,n)$-regularity] of the whole $\mathcal{H}_m^n$-class containing that element as well as the fact that $(m,n)$-regularity and $(m,n)$-right weakly regularity of an element induce the $(m,n)$-regularity and $(m,n)$-right weakly regularity of the whole $\mathcal{B}_m^n$-class and $\mathcal{H}_m^n$-class containing that element, respectively.
کلیدواژه‌ها
Ordered semihypergroups؛ $(m,0)$-hyperideals؛ $(0,n)$-hyperideals

مراجع
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$(m,n)$-Hyperideals in Ordered Semihypergroups