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 $\$\; \backslash bigcap\_p\; pT(G)\; \$$, 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 $\$\; \backslash bigcap\_p\; pG^*\; \$$ is
a nil-ideal in any ring on $G$, and the first Ulm
subgroup $G1$ is its
nilpotent ideal.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k118/k11808h.htm

Last modified: March 23, 2013