Let be a star-operation on and the finite character star-operation induced by . The purpose of this paper is to study when or . In particular, we prove that if every prime ideal of is -invertible, then , and that if is a unique -factorable domain, then is a Krull domain.
Let be the ring of real-valued continuous functions on a frame . In this paper, strongly fixed ideals and characterization of maximal ideals of 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 , is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than...