IMI/Publicaţii/BASM/Ediţii/BASM n.2 (30), 1999/

On product-closed radical classes of abelian groups. (English)

Authors: Gardner B. J.


An example is presented of a set of two torsion-free abelian groups of rank one for which the lower radical class,while closed under countable direct products,is not closed under arbitrary ones.This shows that the product-closed radical classes do not form a sublattice of the lattice of all radical classes of abelian groups.By means of A-radicals,the analogous result for radical classes of associativerings is obtained.There is also some information on the groups which can occur as middle terms of short exact sequences defining radicals by Nunke's construction.

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