English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study prime ideals in skew power series rings $T:=R[[y;\tau,\delta]]$, forsuitably conditioned right noetherian complete semilocal rings $R$,automorphisms $\tau$ of $R$, and $\tau$-derivations $\delta$ of $R$. Theserings were introduced by Venjakob, motivated by issues in noncommutativeIwasawa theory. Our main results concern "Cutting Down" and "Lying Over." Inparticular, under the additional assumption that $\delta = \tau - id$ (a basicfeature of the Iwasawa-theoretic context), we prove: If $I$ is an ideal of $R$,then there exists a prime ideal $P$ of $S$ contracting to $I$ if and only if$I$ is a $\delta$-stable $\tau$-prime ideal of $R$. Our approach essentiallydepends on two key ingredients: First, the algebras considered are zariskian(in the sense of Li and Van Oystaeyen), and so the ideals are all topologicallyclosed. Second, topological arguments can be used to apply previous results ofGoodearl and the author on skew polynomial rings.

On Prime Ideals of Noetherian Skew Power Series Rings