Patch-generated Frames and Projectable Hulls

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Patch-generated Frames and Projectable Hulls
This article considers coherent frame homomorphisms h : L −→ M between coherent frames, which induce an isomorphism between the boolen frames of polars, with M projectable, and such that M is generated by certain complemented elements of M. This abstracts the passage from a semiprime commutative ring with identity to its projectable hull. The frame theoretic setting is investigated thoroughly, first without any assumptions beyond the Zermelo-Fraenkel axioms of set theory, and, subsequently, assuming that algebraic frames are spatial. The culmination of this effort is the result that the spectrum of d-elements of M is obtained from that of L by refining the given hull-kernel topology to the patch topology. The second part of the article relates the projectable hull to the (von Neumann) regular hull, in a variety of contexts, including that of f-rings. For a uniformly complete f-algebra A, it is shown that the maximal -ideals of A that are traces of real maximal ideals of the regu...
Anthony W. Hager, Jorge Martínez
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2007
Where ACS
Authors Anthony W. Hager, Jorge Martínez
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