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Preliminaries on LatticeOrdered Rings and their
Sheaves of LatticeOrdered Rings
The General Representation Theorem
23 other sections not shown
a a b A-ring A-simple belongs locally Boolean space C,-module commutative compact set compact space compact support continuous functions Corollary defined denote derivation law direct factor dominated maximal A-ideals ends the proof epimorphism exists an open finite formal unit functor global sections harmonic algebra Hausdorff space Hence homomorphism implies infer k-algebra lattice lattice-ordered rings Lemma Let us show localizable locally compact locally compact space mapping maximal ideal maximal modular ideal minimal irreducible A-ideal module morphism Neumann algebra obtain obvious open neighborhood open set open subset ordered rings presheaf projection e e proof is ended proper A-ideal quasi-unitary R-module quasicompact REPRESENTATION THEOREM sections with compact semi-simple algebra stalks Stone-Cech compactification strongly semi-simple k-algebra subspace supp p(a surjective Tauberian R-module theory topological space totally ordered totally ordered rings unit element modulo unitary x e P(R