Free profinite p-rings

Mohamed A. Salim; Mihail Ursul

doi:10.1515/form.2011.062

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Free profinite p-rings

Mohamed A. Salim and Mihail Ursul

Published/Copyright: February 25, 2012

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From the journal Volume 24 Issue 2

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.

Keywords.: Profinite ring; free profinite ring; compact ring; prime ring; pro--ring; completed group ring

Received: 2009-06-10

Revised: 2010-04-12

Published Online: 2012-02-25

Published in Print: 2012-March

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Articles in the same Issue

https://doi.org/10.1515/form.2011.062

Keywords for this article

Profinite ring; free profinite ring; compact ring; prime ring; pro--ring; completed group ring