Contribution to study special kinds of hyperideals in ordered semihyperrings

Abstract

In the present paper, we introduce the notion of k-hyperideals on ordered semihyperrings. Then, we investigate some fundamental properties of k-hyperideals of ordered semihyperrings. Indeed, we define (m, n)-hyperideals and (m, n)-bi-hyperideals in ordered semihyperrings and investigate some of their related properties. Moreover, we introduce and analyze the notion of prime (m, n)-bi-hyperideal of an ordered semihyperring.

A Study onA−I−Γ-Hyperideals andm,n−Γ-Hyperfilters in OrderedΓ-Semihypergroups

“…In 2019, Bouaziz and Yaqoob [26] investigated some properties of rough hyperfilters in po-LA-semihypergroups. e notion of (m, n)-hyperideals was introduced in various ordered hyperstructures and had been studied by many authors, for instance, Mahboob et al [27], Omidi and Davvaz [28], and many others.…”

On right chain ordered semihypergroups

“…In 2017, Tang et al [13] introduced and studied the notion of hyper S-posets over an ordered semihypergroup. Omidi and Davvaz [10] introduced and studied the notion of k-hyperideals in ordered semihyperrings as a generalization of k-hyperideals. In [15], Tang and Xie introduced and studied the notion of weakly prime, quasi-prime, quasi-semiprime and weakly quasi-prime left hyperideals in ordered semihypergroups.…”

On phi-2-Absorbing phi‎-2-Absorbing Primary Hyperideals of A Multiplicative Hyperring

“…Later on, it was found that the theory also have many applications in both applied and pure sciences. They can be studied in [5], [8], [11], [6] and [13]. The concept of multiplicative hyperring is introduced and studied by R. Rota [12] in 1982.…”