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D. K. Harrison has shown that if a ring with identity has a positive cone that is an infinite prime (a subsemiring that contains 1 and is maximal with respect to avoiding - 1), and if the cone ...

Let 𝐾 be a number field with algebraic closure K¯, and let 𝑆 be a finite set of places of 𝐾 containing all the infinite ones. Let Γ₀ be a finitely generated subgroup of Gm(K¯), and let Γ⊂Gm(K¯) be ...