FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 8, PAGES 63-76

Absolute nil-ideals of Abelian groups

E. I. Kompantseva

Abstract

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It is known that in an Abelian group G that contains no nonzero divisible torsion-free subgroups the intersection of upper nil-radicals of all the rings on G is $ \bigcap_p pT(G) $, where T(G) is the torsion part of G. In this work, we define a pure fully invariant subgroup G* Ê T(G) of an arbitrary Abelian mixed group G and prove that if G contains no nonzero torsion-free subgroups, then the subgroup $ \bigcap_p pG^* $ is a nil-ideal in any ring on G, and the first Ulm subgroup G1 is its nilpotent ideal.

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Last modified: March 23, 2013