Study on quasi-Γ-hyperideals in Γ-semihypergroups

Abstract

In this paper, we are dealing with [Formula: see text]-semihypergroups which are a generalization of a semigroup, [Formula: see text]-semigroup and a semihypergroup. We introduce the notion of generalized quasi-[Formula: see text]-hyperideal i.e. of [Formula: see text]-quasi-[Formula: see text]-hyperideal, [Formula: see text]-right [Formula: see text]-hyperideal and [Formula: see text]-left [Formula: see text]-hyperideal in [Formula: see text]-semihypergroups and different properties of them and relations between them are studied.

Erratum to “Study on quasi-Γ-hyperideals inΓ-semihypergroups”

“…A Γ -hypersemigroup H is called "regular" [2] In what follows, the aim is to show that is not enough to pass from a semigroup to a hypersemigroup by replacing the multiplication " • " of the semigroup by the hyperoperation " •" and to pass from a hypersemigroup to a Γ -hypersemigroup replacing the " • " by " Γ ". The paper in [2] is the paper in [1] with the only difference that the hypeoperation • in [1] has been replaced by Γ in [2]. Theorem 3.4 in [2] is the Theorem 3.12 in [1].…”

“…The paper in [2] is the paper in [1] with the only difference that the hypeoperation • in [1] has been replaced by Γ in [2]. Theorem 3.4 in [2] is the Theorem 3.12 in [1].…”

“…In fact, Lemma 2.1 in [2] is the Lemma 2.10 in [1]; Proposition 2.1 in [2] is the Proposition 2.11 in [1]; [2] is the Theorem 3.5 in [1]; Corollary 3.1 in [2] is the Corollary 3.6 in [1]; Theorem 3.2 in [2] is the Theorem 3.7 in [1]; Theorem 3.3 in [2] is the Theorem 3.11 in [1]; Theorem 3.4 in [2] is the Theorem 3.12 in [1].…”

“…A Γ -hypersemigroup H is called "regular"[2] if for every x ∈ H there exists y ∈ H such that x ∈ xΓyΓx without any explanation what the xΓyΓx means. What is the xΓyΓx ?…”

Rough prime bi-Γ-hyperideals and fuzzy prime bi- Γ-hyperideals of Γ-semihypergroups

“…A Γ-hyperideal of a Γ-semihypergroup is a generalization of an ideal of a semigroup, a generalization of a hyperideal of a semihypergroup and a generalization of a Γ-ideal of a Γsemigroup. Recently, a lot of other papers [1], [2], [22], [23], [31] studied the structure of Γ-semihypergroups.…”