On Spectral Compactness of Von Neumann Regular Rings

We characterize the spectral compactness of commutative von Neumann regular rings. We show that through a process of adjunction of identity, we can obtain the Alexandroff compactification or a star compactification of the prime spectrum of certain von Neumann regular rings.

On Spectral Compactness of Von Neumann Regular Rings Sobre la compacidad espectral de los anillos regulares de von Neumann IBETH MARCELA RUBIO1, LORENZO ACOSTA2

1Universidad Nacional de Colombia, Bogotá, Colombia. Email:imrubiop@unal.edu.co 
2Universidad Nacional de Colombia, Bogotá, Colombia. Email:lmacostag@unal.edu.co 

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Abstract

We characterize the spectral compactness of commutative von Neumann regular rings. We show that through a process of adjunction of identity, we can obtain the Alexandroff compactification or a star compactification of the prime spectrum of certain von Neumann regular rings.

Key words: Spectral compactness, Prime spectrum, Boolean ring, VonNeumann regular ring, Compactification.

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2000 Mathematics Subject Classification: 13B99, 54B35.

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Resumen

Caracterizamos la compacidad espectral de los anillos regulares de von Neumann conmutativos. Mostramos que a través de un proceso de adjunción de unidad, podemos obtener la compactación de Alexandroff o una compactación estelar del espectro primo de ciertos anillos regulares de von Neumann.

Palabras clave: Compacidad espectral, espectro primo, anillo de Boole, anillo regular de von Neumann, compactación.

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Texto completo disponible en PDF

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References

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(Recibido en enero de 2012. Aceptado en mayo de 2012)

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv46n1a06, 
AUTHOR = {Rubio, Ibeth Marcela and Acosta, Lorenzo}, 
TITLE = {{On Spectral Compactness of Von Neumann Regular Rings}}, 
JOURNAL = {Revista Colombiana de Matemáticas}, 
YEAR = {2012}, 
volume = {46}, 
number = {1}, 
pages = {81--95} 
}