JournalsrsmupVol. 143pp. 135–152

Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame

  • Mostafa Abedi

    Esfarayen University of Technology, Iran
  • Ali Akbar Estaji

    Hakim Sabzevari University, Sabzevar, Iran
Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame cover
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Abstract

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

Cite this article

Mostafa Abedi, Ali Akbar Estaji, Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame. Rend. Sem. Mat. Univ. Padova 143 (2020), pp. 135–152

DOI 10.4171/RSMUP/43