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Let be a semi-prime ideal. Then is called irredundant with respect to if . If is the intersection of all irredundant ideals with respect to , it is called a fixed-place ideal. If there are no irredundant ideals with respect to , it is called an anti fixed-place ideal. We show that each semi-prime ideal has a unique representation as an intersection of a fixed-place ideal and an anti fixed-place ideal. We say the point is a fixed-place point if is a fixed-place ideal. In this situation...
“The kernel functor” from the category of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In , monics are one-to-one, but not necessarily so in LFrm. An embedding for which is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The -objects every embedding of which is KI are characterized;...
Let be a zero-dimensional space and be the set of all continuous real valued functions on with countable image. In this article we denote by (resp., the set of all functions in with compact (resp., pseudocompact) support. First, we observe that (resp., ), where is the Banaschewski compactification of and is the -compactification of . This implies that for an -compact space , the intersection of all free maximal ideals in is equal to , i.e., . By applying methods of functionally...
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