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 R       be a polynomial ring over a field and      M = ⨁  n M n M= \bigoplus _n M_n       be a finitely generated graded      R R      -module, minimally generated by homogeneous elements of degree zero with a graded      R R      -minimal free resolution      F \mathbf {F}      . A Cohen-Macaulay module      M M       is Gorenstein when the graded resolution is symmetric. We give an upper bound for the first Hilbert coefficient,      e 1 e_1       in terms of the shifts in the graded resolution of      M M      . When      M = R / I M = R/I      , a Gorenstein algebra, this bound agrees with the bound obtained in  [ES09]  in Gorenstein algebras with quasi-pure resolution. We conjecture a similar bound for the higher coefficients.

An upper bound for the first Hilbert coefficient of Gorenstein algebras and modules