Strongly fixed ideals in and compact frames

A. A. Estaji; A. Karimi Feizabadi; M. Abedi

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 1, page 1-12
  • ISSN: 0044-8753

Abstract

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Let be the ring of real-valued continuous functions on a frame . In this paper, strongly fixed ideals and characterization of maximal ideals of which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of , is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than spatiality and they are equivalent in the case of conjunctive frames. Assuming Axiom of Choice, compact frames are weakly spatial.

How to cite

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Estaji, A. A., Karimi Feizabadi, A., and Abedi, M.. "Strongly fixed ideals in $ C (L)$ and compact frames." Archivum Mathematicum 051.1 (2015): 1-12. <http://eudml.org/doc/270063>.

@article{Estaji2015,
abstract = {Let $C(L)$ be the ring of real-valued continuous functions on a frame $L$. In this paper, strongly fixed ideals and characterization of maximal ideals of $C(L)$ which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of $C(L)$, is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than spatiality and they are equivalent in the case of conjunctive frames. Assuming Axiom of Choice, compact frames are weakly spatial.},
author = {Estaji, A. A., Karimi Feizabadi, A., Abedi, M.},
journal = {Archivum Mathematicum},
keywords = {frame; ring of real-valued continuous functions; weakly spatial frame; fixed and strongly fixed ideal},
language = {eng},
number = {1},
pages = {1-12},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Strongly fixed ideals in $ C (L)$ and compact frames},
url = {http://eudml.org/doc/270063},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Estaji, A. A.
AU - Karimi Feizabadi, A.
AU - Abedi, M.
TI - Strongly fixed ideals in $ C (L)$ and compact frames
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 1
SP - 1
EP - 12
AB - Let $C(L)$ be the ring of real-valued continuous functions on a frame $L$. In this paper, strongly fixed ideals and characterization of maximal ideals of $C(L)$ which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of $C(L)$, is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than spatiality and they are equivalent in the case of conjunctive frames. Assuming Axiom of Choice, compact frames are weakly spatial.
LA - eng
KW - frame; ring of real-valued continuous functions; weakly spatial frame; fixed and strongly fixed ideal
UR - http://eudml.org/doc/270063
ER -

References

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