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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $(R,\mm,K)$ be a regular local ring containing a field $k$ such thateither char $k=0$ or char $k=p$ and tr-deg $K/\BF_p\geq 1$. Let$g_1,\ldots,g_t$ be regular parameters of $R$ which are linearly independentmodulo $\mm^2$. Let $A=R_{g_1\cdots g_t} [Y_1,\ldots,Y_m,f_1(l_1)^{-1},\ldots,f_n(l_n)^{-1}]$, where $f_i(T)\in k[T]$ and $l_i=a_{i1}Y_1+\ldots+a_{im}Y_m$with $(a_{i1},\ldots,a_{im})\in k^m-(0)$. Then every projective $A$-module ofrank $\geq t$ is free. Laurent polynomial case $f_i(l_i)=Y_i$ of this result isdue to Popescu.

Projective modules over overrings of polynomial rings and a question of Quillen