Discrete and Profinite Modules

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


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).


Inverse Limit Open Subgroup Continuous Homomorphism Inverse System Continuous Section 
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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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