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Discrete and Profinite Modules

  • Luis Ribes
  • Pavel Zalesskii
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 40)

Abstract

A profinite ring Λ is an inverse limit of an inverse system {Λ i ϕ ij } of finite rings. We always assume that rings have an identity element, denoted usually by 1, and that homomorphisms of rings send identity elements to identity elements. A profinite ring Λ is plainly a compact, Hausdorff and totally disconnected topological ring; the converse is also true, as we show in Theorem 5.1.2 below. It is clear that a profinite ring admits a fundamental system of neighborhoods of 0 consisting of open (two-sided) ideals (this follows from a result analogous to Lemma 2.1.1).

Keywords

Inverse Limit Open Subgroup Continuous Homomorphism Inverse System Continuous Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Luis Ribes
    • 1
  • Pavel Zalesskii
    • 2
  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.Department of MathematicsUniversity of BrasiliaBrasiliaBrazil

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