Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings

Given a commutative ring R and S one of its ideals, the function I -- and gt; (I : S) that transforms ideals of R into ideals of R, is right adjoint of the function I -- and gt; IS. We define the S−maximal ideals of R as those ideals J of R such that (J : S) = J. If the ring S is pseudo-regular, the...

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Autores:: Acosta, Lorenzo
Rubio, Marcela

Tipo de recurso:: Article of journal

Fecha de publicación:: 2013

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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spelling	Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Acosta, Lorenzo7a92a4bb-1eb7-4006-9a61-3b673a1c28c9300Rubio, Marcelaf109d580-1170-4ce4-ae9c-c3785e81e91b3002019-07-03T16:59:17Z2019-07-03T16:59:17Z2013https://repositorio.unal.edu.co/handle/unal/73886http://bdigital.unal.edu.co/38363/Given a commutative ring R and S one of its ideals, the function I -- and gt; (I : S) that transforms ideals of R into ideals of R, is right adjoint of the function I -- and gt; IS. We define the S−maximal ideals of R as those ideals J of R such that (J : S) = J. If the ring S is pseudo-regular, then the set of S−maximal ideals of R is a complete lattice, isomorphic to the lattice of the ideals of S. In particular, the annihilator of S in R is the minimum of the S−maximal ideals of R. So the lattice structure of S−maximal ideals of R does not depend on the ring R.On the other hand, the ideals of S can be extended to ideals of R and the ideals of R can be restricted to ideals of S. These two processes are not adjoint to each other, but if we restrict to appropriated collections of ideals we can obtain adjunctions.Dados un anillo conmutativo R y S uno de sus ideales, la función I -- and gt; (I : S), que transforma ideales de R en ideales de R es adjunta a derecha de la función I -- and gt; IS. Se definen los ideales S−maximales de R como aquellos ideales J de R tales que (J : S) = J. Si el anillo S es seudo-regular, entoncesel conjunto de ideales S−maximales de R es un retículo completo, isomorfo al retículo de los ideales de S. En particular, el anulador de S en R es el mínimo de los ideales S−maximales de R. La estructura de retículo de losideales S−maximales de R no depende entonces del anillo R.Por otro lado, los ideales de S se pueden extender a ideales de R y los ideales de R se pueden restringir a ideales de S. Estos dos procesos no son adjuntos entre sí, pero si se restringen a colecciones apropiadas de ideales s´ı se obtienensendas adjunciones.application/pdfspaBoletín de Matemáticashttp://revistas.unal.edu.co/index.php/bolma/article/view/41107Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasBoletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 2357-6529 0120-0380Acosta, Lorenzo and Rubio, Marcela (2013) Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings. Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 2357-6529 0120-0380 .Some adjunctions associated with extensions and restrictions of ideals in the context of commutative ringsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTIdealPrime idealSemi-prime idealOrdered setAdjoint functions.Idealideal primoideal semi-primoconjunto ordenadofunciones adjuntas.ORIGINAL41107-185294-2-PB.pdfapplication/pdf490358https://repositorio.unal.edu.co/bitstream/unal/73886/1/41107-185294-2-PB.pdf874e18a187bcf8d29cf48322aa40bd43MD51THUMBNAIL41107-185294-2-PB.pdf.jpg41107-185294-2-PB.pdf.jpgGenerated Thumbnailimage/jpeg6055https://repositorio.unal.edu.co/bitstream/unal/73886/2/41107-185294-2-PB.pdf.jpgd938dd24f2725f114af31432a0db0023MD52unal/73886oai:repositorio.unal.edu.co:unal/738862024-06-26 23:10:53.62Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
title	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
spellingShingle	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings Ideal Prime ideal Semi-prime ideal Ordered set Adjoint functions. Ideal ideal primo ideal semi-primo conjunto ordenado funciones adjuntas.
title_short	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
title_full	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
title_fullStr	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
title_full_unstemmed	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
title_sort	Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings
dc.creator.fl_str_mv	Acosta, Lorenzo Rubio, Marcela
dc.contributor.author.spa.fl_str_mv	Acosta, Lorenzo Rubio, Marcela
dc.subject.proposal.spa.fl_str_mv	Ideal Prime ideal Semi-prime ideal Ordered set Adjoint functions. Ideal ideal primo ideal semi-primo conjunto ordenado funciones adjuntas.
topic	Ideal Prime ideal Semi-prime ideal Ordered set Adjoint functions. Ideal ideal primo ideal semi-primo conjunto ordenado funciones adjuntas.
description	Given a commutative ring R and S one of its ideals, the function I -- and gt; (I : S) that transforms ideals of R into ideals of R, is right adjoint of the function I -- and gt; IS. We define the S−maximal ideals of R as those ideals J of R such that (J : S) = J. If the ring S is pseudo-regular, then the set of S−maximal ideals of R is a complete lattice, isomorphic to the lattice of the ideals of S. In particular, the annihilator of S in R is the minimum of the S−maximal ideals of R. So the lattice structure of S−maximal ideals of R does not depend on the ring R.On the other hand, the ideals of S can be extended to ideals of R and the ideals of R can be restricted to ideals of S. These two processes are not adjoint to each other, but if we restrict to appropriated collections of ideals we can obtain adjunctions.
publishDate	2013
dc.date.issued.spa.fl_str_mv	2013
dc.date.accessioned.spa.fl_str_mv	2019-07-03T16:59:17Z
dc.date.available.spa.fl_str_mv	2019-07-03T16:59:17Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.identifier.eprints.spa.fl_str_mv	http://bdigital.unal.edu.co/38363/
url	https://repositorio.unal.edu.co/handle/unal/73886 http://bdigital.unal.edu.co/38363/
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.spa.fl_str_mv	http://revistas.unal.edu.co/index.php/bolma/article/view/41107
dc.relation.ispartof.spa.fl_str_mv	Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas Boletín de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv	Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 2357-6529 0120-0380
dc.relation.references.spa.fl_str_mv	Acosta, Lorenzo and Rubio, Marcela (2013) Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings. Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 Boletín de Matemáticas; Vol. 20, núm. 2 (2013); 81-95 2357-6529 0120-0380 .
dc.rights.spa.fl_str_mv	Derechos reservados - Universidad Nacional de Colombia
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institution	Universidad Nacional de Colombia
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Some adjunctions associated with extensions and restrictions of ideals in the context of commutative rings

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