The profinite completion of the integers, the p-adic integers, and Prüfer p-groups
نویسنده
چکیده
By a topological ring we mean a ring X with a Hausdorff topology such that (x, y) 7→ x + y, x 7→ −x, (x, y) 7→ x · y are continuous. A morphism of topological rings is a continuous homomorphism of rings. An inverse system of topological rings is a family of topological rings Xi and a family of morphisms πi,j : Xi → Xj for i, j ∈ I with i ≥ j, such that when i ≥ j ≥ k, πi,k = πj,k ◦ πi,j . If Y is a topological ring, we say that a family of morphisms ψi : Y → Xi is compatible with the inverse system if, whenever i ≥ j,
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