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 L, the ring L of real-valued continuous functions on L is equipped with the uniform topology. The closed ideals of L 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 L, and to characterize pseudocompact frames and Lindelöf frames. It is shown that a frame L is finite if and only if every ideal of L is closed. Finally, we prove that every closed ideal in L is an intersection of maximal ideals.

Publié le :
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
Abedi, Mostafa 1 ; Estaji, Ali Akbar 2

1 Esfarayen University of Technology, Iran
2 Hakim Sabzevari University, Sabzevar, Iran
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     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/}
}
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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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