v-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras

Let n be a fixed natural number. Ternary Menger algebras of rank n, which was established by the authors, can be regarded as a suitable generalization of ternary semigroups. In this article, we introduce the notion of v-regular ternary Menger...

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Autores principales:	Anak Nongmanee, Sorasak Leeratanavalee
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	ternary Menger algebras <i>v</i>-regular ternary Menger algebras left translations Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/30f78eaadc904f069b6c3423548e1e4e
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spelling	oai:doaj.org-article:30f78eaadc904f069b6c3423548e1e4e2021-11-11T18:15:26Z<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras10.3390/math92126912227-7390https://doaj.org/article/30f78eaadc904f069b6c3423548e1e4e2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2691https://doaj.org/toc/2227-7390Let <i>n</i> be a fixed natural number. Ternary Menger algebras of rank <i>n</i>, which was established by the authors, can be regarded as a suitable generalization of ternary semigroups. In this article, we introduce the notion of <i>v</i>-regular ternary Menger algebras of rank <i>n</i>, which can be considered as a generalization of regular ternary semigroups. Moreover, we investigate some of its interesting properties. Based on the concept of <i>n</i>-place functions (<i>n</i>-ary operations), these lead us to construct ternary Menger algebras of rank <i>n</i> of all full <i>n</i>-place functions. Finally, we study a special class of full <i>n</i>-place functions, the so-called left translations. In particular, we investigate a relationship between the concept of full <i>n</i>-place functions and left translations.Anak NongmaneeSorasak LeeratanavaleeMDPI AGarticleternary Menger algebras<i>v</i>-regular ternary Menger algebrasleft translationsMathematicsQA1-939ENMathematics, Vol 9, Iss 2691, p 2691 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	ternary Menger algebras <i>v</i>-regular ternary Menger algebras left translations Mathematics QA1-939
spellingShingle	ternary Menger algebras <i>v</i>-regular ternary Menger algebras left translations Mathematics QA1-939 Anak Nongmanee Sorasak Leeratanavalee <i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
description	Let <i>n</i> be a fixed natural number. Ternary Menger algebras of rank <i>n</i>, which was established by the authors, can be regarded as a suitable generalization of ternary semigroups. In this article, we introduce the notion of <i>v</i>-regular ternary Menger algebras of rank <i>n</i>, which can be considered as a generalization of regular ternary semigroups. Moreover, we investigate some of its interesting properties. Based on the concept of <i>n</i>-place functions (<i>n</i>-ary operations), these lead us to construct ternary Menger algebras of rank <i>n</i> of all full <i>n</i>-place functions. Finally, we study a special class of full <i>n</i>-place functions, the so-called left translations. In particular, we investigate a relationship between the concept of full <i>n</i>-place functions and left translations.
format	article
author	Anak Nongmanee Sorasak Leeratanavalee
author_facet	Anak Nongmanee Sorasak Leeratanavalee
author_sort	Anak Nongmanee
title	<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
title_short	<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
title_full	<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
title_fullStr	<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
title_full_unstemmed	<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras
title_sort	<i>v</i>-regular ternary menger algebras and left translations of ternary menger algebras
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/30f78eaadc904f069b6c3423548e1e4e
work_keys_str_mv	AT anaknongmanee iviregularternarymengeralgebrasandlefttranslationsofternarymengeralgebras AT sorasakleeratanavalee iviregularternarymengeralgebrasandlefttranslationsofternarymengeralgebras
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<i>v</i>-Regular Ternary Menger Algebras and Left Translations of Ternary Menger Algebras

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