Free profinite p-rings

Mohamed A. Salim, Mihail Ursul

Research output: Contribution to journalReview articlepeer-review

Abstract

In this paper, we introduce the notion of a free profinite p-ring over a boolean space (over a set). We prove that free profinite p-rings over infinite boolean spaces (over infinite sets) are prime. As a consequence, we obtain that every profinite pro-p-ring with 1 is a continuous homomorphic image of a profinite prime ring with 1. In addition, we construct examples of profinite prime rings with non-open radical. For a profinite prime ring that satisfies a polynomial identity over its centroid, the radical is open. Furthermore, we prove that every profinite ring of prime characteristic is a subring of a profinite prime ring.

Original languageEnglish
Pages (from-to)303-316
Number of pages14
JournalForum Mathematicum
Volume24
Issue number2
DOIs
Publication statusPublished - Mar 2012

Keywords

  • Compact ring
  • Completed group ring
  • Free profinite ring
  • Prime ring
  • Pro-p-ring
  • Profinite ring

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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