L. Espanol. Dimension of boolean valued lattices and rings. J. Pure Appl. Algebra, pages 223--236, 1986. Home/Search Document Not in Database Summary Related Articles Check |
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An Application of the Constructive Spectrum of a Ring - Persson (Correct)
....truth. Therefore, we will axiomatise P with regards to a distributive lattice hD; i, representing a notion of truth. In this way, the axioms are parametrised on a notion of truth, and for a particular such notion, the axioms can be instantiated. This axiomatisation is due to Joyal [Joy76,Esp86,BV96]. The notion of prime ideal comes together with a subset M of R containing 1 and closed under multiplication, and an ideal I of R such that M I = We fix such an M and I . 4 Definition 6. Let hD; i be a distributive lattice. We call a function z 2 R D a zero if it satisfies the ....
L. Espanol. Dimension of boolean valued lattices and rings. J. Pure Appl. Algebra, pages 223--236, 1986.
A Direct Proof of the Localic Hahn-Banach Theorem - Coquand (1999) (Correct)
....the space associated to B. It is very natural to analyse such situation from a topology without points or localic [Joh82] framework: instead of associating a space, one associates a distributive lattice. This has been done in the case of the spectrum of a ring, by a construction due to A. Joyal [Esp86]. It is shown in [Esp86] how some theorems of commutative algebra become constructive and elementary if understood in such a pointfree way. Another suggestive view is to see this distributive lattice as the (Tarski )Lindenbaum algebra of a propositional theory. The extension theorem mentionned ....
....B. It is very natural to analyse such situation from a topology without points or localic [Joh82] framework: instead of associating a space, one associates a distributive lattice. This has been done in the case of the spectrum of a ring, by a construction due to A. Joyal [Esp86] It is shown in [Esp86] how some theorems of commutative algebra become constructive and elementary if understood in such a pointfree way. Another suggestive view is to see this distributive lattice as the (Tarski )Lindenbaum algebra of a propositional theory. The extension theorem mentionned above becomes then a ....
Luis Espanol. Dimension of boolean valued lattices and rings. J. Pure Appl. Algebra, pages 223--236, 1986.
Valuations and Dedekind's Prague Theorem - Coquand, Persson (Correct)
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L. Espanol. Dimension of boolean valued lattices and rings. J. Pure Appl. Algebra, pages 223--236, 1986.
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