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 study the structure of an idempotent matrix $F$ over a commutative ring.We make explicit the fundamental system of orthogonal idempotents, hidden inthis matrix, for each of which the matrix has a well-defined rank. Similarly wefind a finite number of comaximal elements of the ring which make explicit thefact that the codomain of $F$ is locally free. Our proofs are based on theabstract local-global principle. We give two methods to recover a constructiveproof of these results. The most interesting one is a constructiveinterpretation of a very simple version of the abstract local-global principle.We think we have made a significant step towards a constructive version of the"Hilbert programme" for abstract algebra, i.e. the automatic translation ofproofs of abstract algebra into constructive proofs.

The constructive content of a local-global principle with an application to the structure of a finitely generated projective module