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arXiv · 2610.29712

On unit groups of purely infinite rings

Friedrich Martin Schneider
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Abstract

We prove that the unit group of any purely infinite, regular, right self-injective ring admits a universal sequence of words (thus has strong distortion), is minimally almost periodic, has finite involution width, is verbally simple and verbally elliptic, and has uncountable uniform strong cofinality. These findings are consequences of more refined structural results, some of which provide concrete cardinal estimates involving the Goodearl--Boyle dimension of the ring. A central ingredient in our results is a comprehensive study of bounded normal generation, in particular with respect to certain classes of involutions. Along the way, we develop some abstract methods and concepts pertaining to geometric group theory.

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Friedrich Martin Schneider. 2026-10-21. On unit groups of purely infinite rings. https://arxiv.org/abs/2610.29712

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