All Linear-Solid Varieties of Semirings

A variety of semirings is said to be solid if each of its identities is satisfied as hyperidentity. There are precisely four solid varieties of semirings. Each of them contains every derived algebra, where the both fundamental operations are replaced by arbitrary binary term operations. If a variety...

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Main Authors:	Hounnon Hippolyte, Denecke Klaus
Format:	Article
Language:	English
Published:	Sciendo 2019-06-01
Series:	Discussiones Mathematicae - General Algebra and Applications
Subjects:	variety of semirings hyperidentity linear hypersubstitution solid variety linear-solid variety 08b05 08b15 08a50
Online Access:	https://doi.org/10.7151/dmgaa.1301

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spelling	doaj-37fe5b159c224460943eb5c6cfe5b8282021-09-05T17:19:43ZengSciendoDiscussiones Mathematicae - General Algebra and Applications2084-03732019-06-0139110111210.7151/dmgaa.1301dmgaa.1301All Linear-Solid Varieties of SemiringsHounnon Hippolyte0Denecke Klaus1University of Abomey-Calavi, BeninUniversity of Potsdam, GermanyA variety of semirings is said to be solid if each of its identities is satisfied as hyperidentity. There are precisely four solid varieties of semirings. Each of them contains every derived algebra, where the both fundamental operations are replaced by arbitrary binary term operations. If a variety contains all linear derived algebras, where the fundamental operations are replaced by term operations induced by linear terms, it is called linear-solid. We prove that a variety of semirings is solid if and only if it is linear-solid.https://doi.org/10.7151/dmgaa.1301variety of semiringshyperidentitylinear hypersubstitutionsolid varietylinear-solid variety08b0508b1508a50
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hounnon Hippolyte Denecke Klaus
spellingShingle	Hounnon Hippolyte Denecke Klaus All Linear-Solid Varieties of Semirings Discussiones Mathematicae - General Algebra and Applications variety of semirings hyperidentity linear hypersubstitution solid variety linear-solid variety 08b05 08b15 08a50
author_facet	Hounnon Hippolyte Denecke Klaus
author_sort	Hounnon Hippolyte
title	All Linear-Solid Varieties of Semirings
title_short	All Linear-Solid Varieties of Semirings
title_full	All Linear-Solid Varieties of Semirings
title_fullStr	All Linear-Solid Varieties of Semirings
title_full_unstemmed	All Linear-Solid Varieties of Semirings
title_sort	all linear-solid varieties of semirings
publisher	Sciendo
series	Discussiones Mathematicae - General Algebra and Applications
issn	2084-0373
publishDate	2019-06-01
description	A variety of semirings is said to be solid if each of its identities is satisfied as hyperidentity. There are precisely four solid varieties of semirings. Each of them contains every derived algebra, where the both fundamental operations are replaced by arbitrary binary term operations. If a variety contains all linear derived algebras, where the fundamental operations are replaced by term operations induced by linear terms, it is called linear-solid. We prove that a variety of semirings is solid if and only if it is linear-solid.
topic	variety of semirings hyperidentity linear hypersubstitution solid variety linear-solid variety 08b05 08b15 08a50
url	https://doi.org/10.7151/dmgaa.1301
work_keys_str_mv	AT hounnonhippolyte alllinearsolidvarietiesofsemirings AT deneckeklaus alllinearsolidvarietiesofsemirings
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All Linear-Solid Varieties of Semirings

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