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

We prove that the depth formula holds for two finitely generatedTor-independent modules over Cohen-Macaulay local rings if one of the modulesconsidered has finite reducing projective dimension (for example, if it hasfinite projective dimension, or the ring is a complete intersection). Thisgeneralizes a result of Bergh-Jorgensen which shows that the depth formulaholds for two finitely generated Tor-independent modules over Cohen-Macaulaylocal rings if one of the modules considered has reducible complexity andcertain additional conditions hold.  Each module that has reducible complexity also has finite complexity andfinite reducing projective dimension, but not necessarily vice versa. So a newadvantage we have is that, unlike modules of reducible complexity, Bettinumbers of modules of finite reducing projective dimension can growexponentially.

Depth formula for modules of finite reducing projective dimension