Vol. 297, No. 2, 2018

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Extensions of almost faithful prime ideals in virtually nilpotent mod-$p$ Iwasawa algebras

William Woods

Vol. 297 (2018), No. 2, 477–509

Let G be a nilpotent-by-finite compact p-adic analytic group for some p > 2, and H = FNp(G) be its finite-by-(nilpotent p-valuable) radical. Fix a finite field k of characteristic p, and write kG for the completed group ring of G over k. We show that almost faithful G-stable prime ideals P of kH extend to prime ideals PkG of kG. This is a crucial building block in understanding the prime spectrum of kG.

faithful prime ideals, nilpotent Iwasawa algebras
Mathematical Subject Classification 2010
Primary: 16D25, 16S34, 16S35, 16W60
Received: 12 August 2017
Revised: 26 March 2018
Accepted: 28 April 2018
Published: 20 December 2018
William Woods
School of Mathematics and Statistics
University of Glasgow
United Kingdom