I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2007, VOLUME 13, NUMBER 1, PAGES 229-233
Abelian groups as endomorphic modules over their endomorphism ring
D. S. Chistyakov
O. V. Lyubimcev
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Let be an
associative ring with a unit and be a left
is a near-ring with respect to the
operations of addition and composition and contains the ring
endomorphisms of the -module .
The -module is endomorphic if
We call an Abelian group endomorphic if it is an endomorphic module
over its endomorphism ring.
In this paper, we find endomorphic Abelian groups in the classes of
all separable torsion-free groups, torsion groups, almost completely
decomposable torsion-free groups, and indecomposable torsion-free
groups of rank .
Last modified: December 21, 2006