The p-adic integers as a quotient of a ring of power series
DOI:
https://doi.org/10.15381/pesquimat.v25i1.21522Keywords:
p-adic Integers, Power Seies, Projective Limit, isomorphism, quotientAbstract
Let p a prime number. The most familiar construction of the ring of p-adic integers ℤp, is as the projective limit of quotients of powers of the ideal (p)◁ℤ. There is another description of ℤp as a quotient of the power series ring ℤ[[X]], which can be found in some texts of p-adic analysis (see e.g. [3]). More specifically, there exists a ring isomorphism.
Ψ : ℤ[[X]]/〈p − X〉 → ℤp.
However, this isomorphism is also topological in nature, but there is no proof of this fact in the corresponding literature. In this article we will prove in sufficient detail that the above description is also valid in the context of topological rings.
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Copyright (c) 2022 Napoleón Caro Tuesta, Alex Molina Sotomayor, Mario Enrique Santiago Saldaña
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