On the structure of quasi-hyperideals and bi-hyperideals in ternary semihypergroups

Naka, Krisanthi; Hila, Kostaq

doi:10.1007/s13370-014-0306-3

Cited by 12 publications

(4 citation statements)

References 17 publications

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“…[3,4,5,6,14]). Recently, Hila et al [10,11], Naka et al [21,22,23,24] and Mani et al [19] have studied the ternary semihypergroups in terms of hyperideals and quasi(bi)-hyperideals.…”

Section: Introductionmentioning

confidence: 99%

Semipseudosymmetric hyperideals in ternary semihypergroups

Yella

Mani

Hila

et al. 2022

AUCMCS

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The main objective of this study is to introduce a new class of hyperideals called pseudosymmetric and semipseudosymmetric hyperideals in ternary semihypergroups. We try to investigate the properties of these hyperideals by giving some suitable examples for the same. In particular we prove that every pseudosymmetric hyperideal of a ternary semihypergroups is a semipseudosymmetric hyperideal. We study the fundamental relations among these hyperideals and provide few results.

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“…[3,4,5,6,14]). Recently, Hila et al [10,11], Naka et al [21,22,23,24] and Mani et al [19] have studied the ternary semihypergroups in terms of hyperideals and quasi(bi)-hyperideals.…”

Section: Introductionmentioning

confidence: 99%

Semipseudosymmetric hyperideals in ternary semihypergroups

Yella

Mani

Hila

et al. 2022

AUCMCS

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“…The interesting properties of j-hyperideals in ternary semihypergroups and n-ary semihypergroups can be found in [26,27]. The left regularity, right regularity, intra-regularity, and complete regularity of ternary semihypergroups in terms of various j-hyperideals were characterized by Naka et al [28,29]. Moreover, several kinds of regularity of ordered ternary semihypergroups have been investigated by Basar et al [30] and Talee et al [31].…”

Section: Introductionmentioning

confidence: 99%

Regularities in Ordered n-Ary Semihypergroups

Daengsaen

Leeratanavalee

2021

Mathematics

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This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1≤j≤n and n≥3. We first introduce the notion of (softly) left regularity, (softly) right regularity, (softly) intra-regularity, complete regularity, generalized regularity of ordered n-ary semihypergroups and investigate their related properties. Several characterizations of them in terms of j-hyperideals are provided. Finally, the relationships between various classes of regularities in ordered n-ary semihypergroups are also established.

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“…The algebraic hyperstructures represent a natural generalization of classical algebraic structures which is based on the notion of hyperoperation introduced by the French mathematician Marty [11] in 1934. Hila et al [6,13,14,15] provided some results on ternary semihypergroups. Chavlina [3] introduced the concept of ordering hypergroups as a special class of hypergroups.…”

Section: Introductionmentioning

confidence: 99%

Int-soft bi-hyperideals in ordered ternary semihypergroups

Talee

Abbasi

Hila

2021

AUCMCS

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The aim of this paper is to study po-ternary semihypergroups in terms of the int-soft bi-hyperideals. We introduce the notion of int-soft bi-hyperideals in po-ternary semihypergroups and some properties of them are investigated. Characterizations of bi-hyperideals in terms of int-soft bi-hyperideals are obtained. We prove that every int-soft hyperideal is an int-soft bi-hyperideal but the converse is not true. Examples are provided to illustrate the results.

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On the structure of quasi-hyperideals and bi-hyperideals in ternary semihypergroups

Cited by 12 publications

References 17 publications

Semipseudosymmetric hyperideals in ternary semihypergroups

Semipseudosymmetric hyperideals in ternary semihypergroups

Regularities in Ordered n-Ary Semihypergroups

Int-soft bi-hyperideals in ordered ternary semihypergroups

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