Reversible Rings with Involutions and Some Minimalities

In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, ∗-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and exam...

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Detalles Bibliográficos
Autores principales: Fakieh, W. M., Nauman, S. K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3893010/
https://www.ncbi.nlm.nih.gov/pubmed/24489510
http://dx.doi.org/10.1155/2013/650702
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author Fakieh, W. M.
Nauman, S. K.
author_facet Fakieh, W. M.
Nauman, S. K.
author_sort Fakieh, W. M.
collection PubMed
description In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, ∗-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of ∗-reversible rings. It is proved here that the polynomial rings of ∗-reversible rings may not be ∗-reversible. A criterion for rings which cannot adhere to any involution is developed and it is observed that a minimal noninvolutary ring is of order 4 and that a minimal noncommutative ∗-reversible ring is of order 16.
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spelling pubmed-38930102014-02-02 Reversible Rings with Involutions and Some Minimalities Fakieh, W. M. Nauman, S. K. ScientificWorldJournal Research Article In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, ∗-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of ∗-reversible rings. It is proved here that the polynomial rings of ∗-reversible rings may not be ∗-reversible. A criterion for rings which cannot adhere to any involution is developed and it is observed that a minimal noninvolutary ring is of order 4 and that a minimal noncommutative ∗-reversible ring is of order 16. Hindawi Publishing Corporation 2013-12-30 /pmc/articles/PMC3893010/ /pubmed/24489510 http://dx.doi.org/10.1155/2013/650702 Text en Copyright © 2013 W. M. Fakieh and S. K. Nauman. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Fakieh, W. M.
Nauman, S. K.
Reversible Rings with Involutions and Some Minimalities
title Reversible Rings with Involutions and Some Minimalities
title_full Reversible Rings with Involutions and Some Minimalities
title_fullStr Reversible Rings with Involutions and Some Minimalities
title_full_unstemmed Reversible Rings with Involutions and Some Minimalities
title_short Reversible Rings with Involutions and Some Minimalities
title_sort reversible rings with involutions and some minimalities
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3893010/
https://www.ncbi.nlm.nih.gov/pubmed/24489510
http://dx.doi.org/10.1155/2013/650702
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AT naumansk reversibleringswithinvolutionsandsomeminimalities

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