Geodesic
Strongly fixed ideals in $ C (L)$ and compact frames
Archivum mathematicum, Tome 51 (2015) no. 1, pp. 1-12
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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.
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.
DOI : 10.5817/AM2015-1-1
Classification : 06D22, 13A15, 13C99
Keywords: frame; ring of real-valued continuous functions; weakly spatial frame; fixed and strongly fixed ideal 
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Estaji, A. A.; Karimi Feizabadi, A.; Abedi, M. Strongly fixed ideals in $ C (L)$ and compact frames. Archivum mathematicum, Tome 51 (2015) no. 1, pp. 1-12. doi: 10.5817/AM2015-1-1

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