On polynomial equation rings and radicals
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.6/9663 |
Resumo: | The notion of n-polynomial equation ring, for an arbitrary but fixed positive integer n, is introduced. A ring A is called an n- polynomial equation ring if γ(A[Xn]) = γ(A)[ Xn], for all radicals γ. If this equation holds for all hereditary radicals γ, then A is said to be a hereditary n-polynomial equation ring. Various characterizations of these rings are provided. It is shown that, for any ring A, the zero-ring on the additive group of A is an n- polynomial equation ring and that any Baer radical ring is a hereditary n- polynomial equation ring. New radicals based on these notions are introduced, one of which is a special radical with a polynomially extensible semisimple class. |
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On polynomial equation rings and radicalsAmitsur ringsHereditary Amitsur ringsRadicalsRadicals with the Amitsur propertyThe notion of n-polynomial equation ring, for an arbitrary but fixed positive integer n, is introduced. A ring A is called an n- polynomial equation ring if γ(A[Xn]) = γ(A)[ Xn], for all radicals γ. If this equation holds for all hereditary radicals γ, then A is said to be a hereditary n-polynomial equation ring. Various characterizations of these rings are provided. It is shown that, for any ring A, the zero-ring on the additive group of A is an n- polynomial equation ring and that any Baer radical ring is a hereditary n- polynomial equation ring. New radicals based on these notions are introduced, one of which is a special radical with a polynomially extensible semisimple class.Taylor & FrancisuBibliorumMendes, D. I. C.Ochirbat, B.Tumurbat, S.2020-03-02T16:45:03Z2019-09-272019-09-27T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.6/9663eng10.2989/16073606.2019.1654552metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-12-15T09:50:46Zoai:ubibliorum.ubi.pt:10400.6/9663Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:49:42.970150Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
On polynomial equation rings and radicals |
title |
On polynomial equation rings and radicals |
spellingShingle |
On polynomial equation rings and radicals Mendes, D. I. C. Amitsur rings Hereditary Amitsur rings Radicals Radicals with the Amitsur property |
title_short |
On polynomial equation rings and radicals |
title_full |
On polynomial equation rings and radicals |
title_fullStr |
On polynomial equation rings and radicals |
title_full_unstemmed |
On polynomial equation rings and radicals |
title_sort |
On polynomial equation rings and radicals |
author |
Mendes, D. I. C. |
author_facet |
Mendes, D. I. C. Ochirbat, B. Tumurbat, S. |
author_role |
author |
author2 |
Ochirbat, B. Tumurbat, S. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
uBibliorum |
dc.contributor.author.fl_str_mv |
Mendes, D. I. C. Ochirbat, B. Tumurbat, S. |
dc.subject.por.fl_str_mv |
Amitsur rings Hereditary Amitsur rings Radicals Radicals with the Amitsur property |
topic |
Amitsur rings Hereditary Amitsur rings Radicals Radicals with the Amitsur property |
description |
The notion of n-polynomial equation ring, for an arbitrary but fixed positive integer n, is introduced. A ring A is called an n- polynomial equation ring if γ(A[Xn]) = γ(A)[ Xn], for all radicals γ. If this equation holds for all hereditary radicals γ, then A is said to be a hereditary n-polynomial equation ring. Various characterizations of these rings are provided. It is shown that, for any ring A, the zero-ring on the additive group of A is an n- polynomial equation ring and that any Baer radical ring is a hereditary n- polynomial equation ring. New radicals based on these notions are introduced, one of which is a special radical with a polynomially extensible semisimple class. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-09-27 2019-09-27T00:00:00Z 2020-03-02T16:45:03Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.6/9663 |
url |
http://hdl.handle.net/10400.6/9663 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.2989/16073606.2019.1654552 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Taylor & Francis |
publisher.none.fl_str_mv |
Taylor & Francis |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136388426235904 |