Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame
Rendiconti del Seminario Matematico della Università di Padova, Tome 143 (2020), pp. 135-152.
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For a completely regular frame , the ring of real-valued continuous functions on is equipped with the uniform topology. The closed ideals of in this topology are studied, and a new, merely algebraic characterization of these ideals is given. This result is used to describe the real ideals of , and to characterize pseudocompact frames and Lindelöf frames. It is shown that a frame is finite if and only if every ideal of is closed. Finally, we prove that every closed ideal in is an intersection of maximal ideals.
Publié le :
DOI : 10.4171/RSMUP/43
DOI : 10.4171/RSMUP/43
Classification :
06, 13, 16, 54
Mots clés : Closed ideal, uniform topology, frame, ring of all real-valued continuous functions on a frame, $\omega$-divisible ideal, pseudocompact frame, Lindelöf frame
Mots clés : Closed ideal, uniform topology, frame, ring of all real-valued continuous functions on a frame, $\omega$-divisible ideal, pseudocompact frame, Lindelöf frame
Affiliations des auteurs :
Abedi, Mostafa 1 ;
Estaji, Ali Akbar 2
@article{RSMUP_2020__143__135_0,
author = {Abedi, Mostafa and Estaji, Ali Akbar},
title = {Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {135--152},
publisher = {European Mathematical Society Publishing House},
address = {Zuerich, Switzerland},
volume = {143},
year = {2020},
doi = {10.4171/RSMUP/43},
mrnumber = {4103743},
zbl = {1481.06029},
url = {http://www.numdam.org/articles/10.4171/RSMUP/43/}
}
TY - JOUR AU - Abedi, Mostafa AU - Estaji, Ali Akbar TI - Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2020 SP - 135 EP - 152 VL - 143 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/43/ DO - 10.4171/RSMUP/43 ID - RSMUP_2020__143__135_0 ER -
%0 Journal Article %A Abedi, Mostafa %A Estaji, Ali Akbar %T Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame %J Rendiconti del Seminario Matematico della Università di Padova %D 2020 %P 135-152 %V 143 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/43/ %R 10.4171/RSMUP/43 %F RSMUP_2020__143__135_0
Abedi, Mostafa; Estaji, Ali Akbar. Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame. Rendiconti del Seminario Matematico della Università di Padova, Tome 143 (2020), pp. 135-152. doi : 10.4171/RSMUP/43. http://www.numdam.org/articles/10.4171/RSMUP/43/
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