<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0121-7488</journal-id>
<journal-title><![CDATA[Ciencia en Desarrollo]]></journal-title>
<abbrev-journal-title><![CDATA[Ciencia en Desarrollo]]></abbrev-journal-title>
<issn>0121-7488</issn>
<publisher>
<publisher-name><![CDATA[Universidad Pedagógica y Tecnológica de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-74882024000100097</article-id>
<article-id pub-id-type="doi">10.19053/01217488.v15.n1.2024.15963</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Anillo no local inmerso en un producto de cuerpos]]></article-title>
<article-title xml:lang="en"><![CDATA[Non-local ring embedded in a direct product of fields]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Granados-Pinzon]]></surname>
<given-names><![CDATA[Claudia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Contreras-Mendoza]]></surname>
<given-names><![CDATA[Astrid L.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Olaya-Leon]]></surname>
<given-names><![CDATA[Wilson]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<volume>15</volume>
<numero>1</numero>
<fpage>97</fpage>
<lpage>103</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-74882024000100097&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-74882024000100097&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-74882024000100097&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo estudiamos la inmersión de R, un anillo conmutativo con unidad no local, en un producto directo de cuerpos. En el producto de los cuerpos cocientes de R dados por sus ideales maximales. El homomorfismo &#966; de R en el producto directo de cuerpos cocientes está definido por la propiedad universal del producto y su nucleo es Ker&#966;   = (R), donde  (R) es el radical de Jacobson de R. Si  (R) = {0}, el homomorfismo es inyectivo en el caso infinito, y en el caso finito probaremos que &#966; es un isomorfismo. Además, consideramos el caso donde R es un anillo total de fracciones con un número finito de ideales maximales y mostraremos que el homomorfismo de R en el producto de sus localizados es inyectivo. Más aún, si R es de la forma &#8484;n, con  n &#8800; 0, o R es un K-algebra finita, con K un cuerpo, tenemos que este homomorfismo es un isomorfismo.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper we study the immersion of a non-local commutative ring with unity R into a direct product of fields. In the product of quotient fields defined by the maximal ideals of R. The ring homomorphism &#966; from R into direct product of quotient fields is defined by the universal property of the direct product. Let Ker&#966; be the kernel of &#966;, then Ker&#966; =  (R), where  (R) is the Jacobson radical of the ring R. If  (R) = {0}, the ring homomorphism is injective in the infinite case and in the finite case, we will proof &#966; is an isomorphism. In addition, we consider R a total ring of fractions with finite mimber of maximal ideals and show that the ring homomorphism from R into a direct product of localizations is injective. Even more, if R have the form &#8484;n, with n  &#8800; 0, or R is a finite dimensional K-algebra with K a field, we have that this ring homomorphism is an isomorphism.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Anillo total de fracciones]]></kwd>
<kwd lng="es"><![CDATA[cuerpo cociente]]></kwd>
<kwd lng="es"><![CDATA[K-algebra finita]]></kwd>
<kwd lng="es"><![CDATA[localización]]></kwd>
<kwd lng="es"><![CDATA[producto directo de anillos]]></kwd>
<kwd lng="es"><![CDATA[radical de Jacobson]]></kwd>
<kwd lng="en"><![CDATA[Total ring of fractions]]></kwd>
<kwd lng="en"><![CDATA[field of fractions]]></kwd>
<kwd lng="en"><![CDATA[finite dimensional K-algebra]]></kwd>
<kwd lng="en"><![CDATA[localization]]></kwd>
<kwd lng="en"><![CDATA[direct product of rings]]></kwd>
<kwd lng="en"><![CDATA[Jacobson radical]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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