Existence of proper semihypergroups of type U on the right

Fasino, Dario; Freni, Domenico

doi:10.1016/j.disc.2007.03.001

Cited by 35 publications

(20 citation statements)

References 6 publications

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“…As a consequence, not only all hypergroups are simple semihypergroups, but also all finite semihypergroups of type U on the right are simple, because they are left-reproducible [8,9,13]. 2.…”

Section: Definition 22mentioning

confidence: 99%

Fundamental relations in simple and 0-simple semihypergroups of small size

Fasino

Freni

2012

Arab. J. Math.

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We consider the fundamental relations β and γ in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where β is not transitive, apart of isomorphisms. Moreover, we show that the least order for which there exists a strongly simple semihypergroup where β is not transitive is 4. Finally, we prove that γ is transitive in all simple semihypergroups, and determine necessary and sufficient conditions for a 0-simple semihypergroup to have γ transitive. The latter results obviously hold also for simple and 0-simple semigroups. Mathematics Subject Classification (2010) 20N20 · 05A99

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Section: Definition 22mentioning

confidence: 99%

Fundamental relations in simple and 0-simple semihypergroups of small size

Fasino

Freni

2012

Arab. J. Math.

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“…The theory of suitable modified hyperstructures can serve as a mathematical background in the field of quantum communication systems. Some principal notions about semihypergroups theory can be found in [3,6,13,14,17,25,42,50]. Recently, Davvaz, Hila and et.…”

Section: Introductionmentioning

confidence: 99%

Some properties of hyperideals in ternary semihypergroups

Naka

Hila

2013

Mathematica Slovaca

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ABSTRACT. Ternary semihypergroups are algebraic structures with one ternary associative hyperoperation. In this paper we give some properties of left (right) and lateral hyperideals in ternary semihypergroups. We introduce the notion of left simple, lateral simple, left (0-)simple and lateral 0-simple ternary semihypergroups and characterize the minimality and maximality of left (right) and lateral hyperideals in ternary semihypergroups. The relationship between them is investigated in ternary semihypergroups extending and generalizing the analogues results for ternary semigroups.

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“…The study on the theory of semihypergroups is one of the most active subjects in algebraic hyperstructure theory. Nowadays, many researchers studied different aspects of semihypergroups, for instance, Anvariyeh et al [1], Chaopraknoi and Triphop [5], Davvaz [8], Hila et al [14], Leoreanu [20] and Salvo et al [25], also see [11,24]. A theory of hyperstructures on ordered semigroups has been recently developed.…”

Section: Introductionmentioning

confidence: 99%

An investigation on hyper S-posets over ordered semihypergroups

2017

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Abstract:In this paper, we define and study the hyper S-posets over an ordered semihypergroup in detail. We introduce the hyper version of a pseudoorder in a hyper S-poset, and give some related properties. In particular, we characterize the structure of factor hyper S-posets by pseudoorders. Furthermore, we introduce the concepts of order-congruences and strong order-congruences on a hyper S -poset A; and obtain the relationship between strong order-congruences and pseudoorders on A. We also characterize the (strong) order-congruences by the -chains, where is a (strong) congruence on A. Moreover, we give a method of constructing order-congruences, and prove that every hyper S -subposet B of a hyper S -poset A is a congruence class of one order-congruence on A if and only if B is convex. In the sequel, we give some homomorphism theorems of hyper S-posets, which are generalizations of similar results in S -posets and ordered semigroups.

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Existence of proper semihypergroups of type U on the right

Cited by 35 publications

References 6 publications

Fundamental relations in simple and 0-simple semihypergroups of small size

Fundamental relations in simple and 0-simple semihypergroups of small size

Some properties of hyperideals in ternary semihypergroups

An investigation on hyper S-posets over ordered semihypergroups

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