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On product-closed radical classes of abelian groups. (English)
Authors: Gardner B. J.
Abstract
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.School of Mathematics University of Tasmania
GPO Box 252-37, Hobart, Tasmania 7001, Australia
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GPO Box 252-37, Hobart, Tasmania 7001, Australia
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Contents
- To the 35th anniversary of the Institute of Mathematics and Computer Science of the Academy of Sciences of the Republic of Moldova.
- On coverings in the lattice of linear topologies. (English)
- Radical assignments and radical classes. (English)
- On rings with a distributive lattice of pretorsions. (Russian)
- On product-closed radical classes of abelian groups. (English)
- Some remarks concerning nuclei on semiring. (English)
- The classes of divisible and reduced modules associated to the torsion theories. (English)
- Zero divisors in group-based algebras. Algebras without zero divisors. (English)
- Category of representations of elementary knowledge. (English)
- On endomorphism rimgs without nonzero nilpotent elements. II. (English)
- On the intersection of radical classes. (English)
- Vladimir Ivanovich Arnautov. A tribute in honor of his 60th birthday.
