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

Given a finite group  G  and a field  F  of characteristic zero, we let    F   〈    x   1  ,   g  1,  …  ,   x   r  ,   g  r〉be the free  G ‐graded  F ‐algebra generated by homogeneous variables{    x   i  ,   g  i}g  i∊  G   . Let ℐ be a  G ‐graded  T ‐ideal of    F   〈    x   1  ,   g  i,  …  ,   x   r  ,   g  r〉which is PI (that is, the algebra    F   〈    x   1  ,   g  i,  …  ,   x   r  ,   g  r〉   /  ℐ   . We prove that the Hilbert series of    F   〈    x   1  ,   g  i,  …  ,   x   r  ,   g  r〉   /  ℐ    is a rational function. More generally, we show that the Hilbert series which corresponds to any  g ‐homogeneous component of    F   〈    x   1  ,   g  i,  …  ,   x   r  ,   g  r〉   /  ℐ    is a rational function.

Hilbert series of PI relatively free G ‐graded algebras are rational functions