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

William Woods

doi:10.2140/pjm.2018.297.477

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

William Woods

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let G be a nilpotent-by-finite compact p-adic analytic group for some p > 2, and H = FN_p(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.

Original language	English
Pages (from-to)	477-509
Number of pages	33
Journal	Pacific Journal of Mathematics
Volume	297
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2018.297.477
State	Published - 1 Jan 2018
Externally published	Yes

Keywords

Faithful prime ideals
Nilpotent Iwasawa algebras

ASJC Scopus subject areas

General Mathematics

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10.2140/pjm.2018.297.477

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abstract = "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.",

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AB - 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.

KW - Faithful prime ideals

KW - Nilpotent Iwasawa algebras

UR - https://www.scopus.com/pages/publications/85059653697

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DO - 10.2140/pjm.2018.297.477

M3 - Article

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JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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