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/

Zendy Plus

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

Zendy Tools

Zendy Open

The non-trivial hereditary monocoreflective subcategories of the Abelian groups are the following ones: {G ∈ Ob Ab | G is a torsion group, and for all g ∈ G the exponent of any prime p in the prime factorization of o(g) is at most E(p)}, where E(·) is an arbitrary function from the prime numbers to {0, 1, 2, …,∞}. (o(·) means the order of an element, and n ≤ ∞ means n < ∞.) This result is dualized to the category of compact Hausdorff Abelian groups (the respective subcategories are {G ∈ Ob CompAb | G has a neighbourhood subbase {Gα} at 0, consisting of open subgroups, such that G/Gα is cyclic, of order like o(g) above}), and is generalized to categories of unitary R-modules for R an integral domain that is a principal ideal domain. For general rings R with 1, an analogous theorem holds, where the hereditary monocoreflective subcategories of unitary left R-modules are described with the help of filters L in the lattice of the left ideals of the ring R. These subcategories consist of those left R-modules, for which the annihilators of all elements belong to L. If R is commutative, then this correspondence between these subcategories and these filters L is bijective.

The hereditary monocoreflective subcategories of Abelian groups and R-modules