#### Vol. 297, No. 2, 2018

 Recent Issues Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Vol. 296: 1  2 Vol. 295: 1  2 Vol. 294: 1  2 Vol. 293: 1  2 Vol. 292: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals
Extensions of almost faithful prime ideals in virtually nilpotent mod-$p$ Iwasawa algebras

### William Woods

Vol. 297 (2018), No. 2, 477–509
##### Abstract

Let $G$ be a nilpotent-by-finite compact $p$-adic analytic group for some $p>2$, and $H={FN}_{p}\left(G\right)$ 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 $kG$.

##### Keywords
faithful prime ideals, nilpotent Iwasawa algebras
##### Mathematical Subject Classification 2010
Primary: 16D25, 16S34, 16S35, 16W60