Radical ideals and coherent frames

Bernhard Banaschewski

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 349-370
  • ISSN: 0010-2628

Abstract

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It follows from Stone Duality that Hochster's results on the relation between spectral spaces and prime spectra of rings translate into analogous, formally stronger results concerning coherent frames and frames of radical ideals of rings. Here, we show that the latter can actually be obtained without Stone Duality, proving them in Zermelo-Fraenkel set theory and thereby sharpening the original results of Hochster.

How to cite

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Banaschewski, Bernhard. "Radical ideals and coherent frames." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 349-370. <http://eudml.org/doc/247876>.

@article{Banaschewski1996,
abstract = {It follows from Stone Duality that Hochster's results on the relation between spectral spaces and prime spectra of rings translate into analogous, formally stronger results concerning coherent frames and frames of radical ideals of rings. Here, we show that the latter can actually be obtained without Stone Duality, proving them in Zermelo-Fraenkel set theory and thereby sharpening the original results of Hochster.},
author = {Banaschewski, Bernhard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {coherent frame or locale; radical ideal; prime spectrum; spectral space; support on a ring; Boolean powers; spectral spaces; radical ideals; coherent frames},
language = {eng},
number = {2},
pages = {349-370},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Radical ideals and coherent frames},
url = {http://eudml.org/doc/247876},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Banaschewski, Bernhard
TI - Radical ideals and coherent frames
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 349
EP - 370
AB - It follows from Stone Duality that Hochster's results on the relation between spectral spaces and prime spectra of rings translate into analogous, formally stronger results concerning coherent frames and frames of radical ideals of rings. Here, we show that the latter can actually be obtained without Stone Duality, proving them in Zermelo-Fraenkel set theory and thereby sharpening the original results of Hochster.
LA - eng
KW - coherent frame or locale; radical ideal; prime spectrum; spectral space; support on a ring; Boolean powers; spectral spaces; radical ideals; coherent frames
UR - http://eudml.org/doc/247876
ER -

References

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  1. Hochster M., Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43-60. (1969) Zbl0184.29401MR0251026
  2. Hodges W., Krull implies Zorn, J. London Math. Soc. 19 (1979), 285-287. (1979) Zbl0394.03045MR0533327
  3. Johnstone P.T., Stone Spaces, Cambridge University Press, Cambridge, 1982. Zbl0586.54001MR0698074
  4. Vermeulen J.J.C., A localic proof of Hochster's Theorem, unpublished draft, University of Cape Town, 1992. 

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