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On atomic ideals in some factor rings of C ( X , )

Alireza Olfati (2021)

Commentationes Mathematicae Universitatis Carolinae

A nonzero R -module M is atomic if for each two nonzero elements a , b in M , both cyclic submodules R a and R b have nonzero isomorphic submodules. In this article it is shown that for an infinite P -space X , the factor rings C ( X , ) / C F ( X , ) and C c ( X ) / C F ( X ) have no atomic ideals. This fact generalizes a result published in paper by A. Mozaffarikhah, E. Momtahan, A. R. Olfati and S. Safaeeyan (2020), which says that for an infinite set X , the factor ring X / ( X ) has no atomic ideal. Another result is that for each infinite P -space X , the...

On binary coproducts of frames

Xiangdong Chen (1992)

Commentationes Mathematicae Universitatis Carolinae

The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms.

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