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

In this note, we establish conditions under which the union of an increasingsequence of completely decomposable modules over domains are again completelydecomposable. In our investigation, the condition of purity of modules iscrucial. In fact, the main result reported in this work states that a module iscompletely decomposable when it is the union of a countable, ascending chain ofcompletely decomposable, pure submodules, providing thus a generalization ofHill's criterion of freeness from abelian group theory.

A note on the direct limit of increasing sequences of completely decomposable modules over integral domains