ABSTRACT. Properties of abelian groups related to a given finite rank torsion free abelian group A ate analyzed in terms of End (A ), the endomorphism ring of A. This point of view gives rise to generalizations of some classical theorems by R. Baer and examples of pathological direct sum decompositions of finite rank torsion free abelian groups.
ABSTRACT. Properties of abelian groups related to a given finite rank torsion free abelian group A ate analyzed in terms of End (A ), the endomorphism ring of A. This point of view gives rise to generalizations of some classical theorems by R. Baer and examples of pathological direct sum decompositions of finite rank torsion free abelian groups.
A finite rank torsion free abelian group G is almost completely decomposable if there exists a completely decomposable subgroup C with finite index in G. The minimum of [G: C] over all completely decomposable subgroups C of G is denoted by ¿(G). An almost completely decomposable group G has, up to isomorphism, only finitely many summands. If ¿(G) is a prime power, then the rank 1 summands in any decomposition of G as a direct sum of indecomposable groups are uniquely
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