*-Relations on ternary semigroups

Ashrafi, Nahid; Yazdanmehr, Zahra

doi:10.1142/s0219887818500949

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…Previously, in 1904, Kanser, E. [13] presented the so-called n-ary algebras, which is the extension of the group concept (cf. [14]). According to ternary algebraic structures and its generalization, the so-called n-ary algebraic structures, raise certain hopes in view of their applications in Physics.…”

Section: Introductionmentioning

confidence: 99%

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Ternary Menger Algebras: A Generalization of Ternary Semigroups

Nongmanee

Leeratanavalee

2021

Mathematics

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Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.

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Section: Introductionmentioning

confidence: 99%

“…Based on the concept of covering groups, Santiago, M. L. and Sri Bala, S. [43] constructed the semigroup S T such that a ternary semigroup T embedded in S T , and investigated some related properties in 2010. Recently, congruences and some different types of congruences on ternary semigroups are presented in [14,34,44,45].…”

Section: Introductionmentioning

confidence: 99%

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Nongmanee

Leeratanavalee

2021

Mathematics

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Representations, Translations and Reductions for Ternary Semihypergroups

Nongmanee

Leeratanavalee

2022

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The concept of ternary semihypergroups can be considered as a natural generalization of arbitrary ternary semigroups. In fact, each ternary semigroup can be constructed to a ternary semihypergroup. In this article, we investigate some interesting algebraic properties of ternary semihypergroups induced by semihypergroups. Then, we extend the well-known result on group theory and semigroup theory, the so-called Cayley’s theorem, to study on ternary semihypergroups. This leads us to construct the ternary semihypergroups of all multivalued full binary functions. In particular, we investigate that each element of a ternary semihypergroup induced by a semihypergroup can be represented by a multivalued full binary function. Moreover, we introduce the concept of translations for ternary semihypergroups which can be considered as a generalization of translations on ternary semigrgoups. Then, we construct ternary semihypergroups of all multivalued full functions and ternary semihypergroups via translations. So, some interesting algebraic properties are investigated. At the last section, we discover that there are ternary semihypergroups satisfying some significant conditions which can be reduced to semihypergroups. Furthermore, ternary semihypergroups with another one condition can be reduced to idempotent semihypergroups.

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*-Relations on ternary semigroups

Cited by 2 publications

References 6 publications

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Representations, Translations and Reductions for Ternary Semihypergroups

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