Non-local ring embedded in a direct product of fields
- Claudia Granados Pinzón
, - Astrid L. Contreras-Mendoza ,
- Wilson Olaya-Le´on
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
ϕ from R into direct product of quotient fields is defined by the universal property of the direct product.
Let Kerϕ be the kernel of ϕ, then Kerϕ = J (R), with J (R) is the Jacobson radical of the ring R. If
J (R) = {0}, the ring homomorphism is injective in the infinite case and in the finite case, we will proof ϕ
is an isomorphism. In addition, we consider R a total ring of fractions with finite number of maximal ideals
and will show that the ring homomorphism from R into a direct product of localizations is injective. Even
more, if R have the form Zn, with n ̸= 0, or R is a finite dimensional K−algebra with field K, we have that
this ring homomorphism is an isomorphism.
Keywords
Total ring of fractions, field of fractions, finite dimensional K−algebra, localization, direct product of rings, Jacobson radical.
Author Biography
Claudia Granados Pinzón
Doctora en Matemáticas Universidad de Valladolid (España)
C.C. 63514588
Fecha de Nacimiento: 3 de septiembre de 1976
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