Abstract
This paper compares of the rank of a torsion-free Abelian group G of finite rank and the rank of its endomorphism ring E(G) under the condition that E(G) is commutative. In particular, if G is strongly indecomposable such that E(G) is commutative and is flat as a -module, then r0(E(G)) ≤ r0(G). On the other hand, we provide examples that, in general, the rank of E(G) can be any number between 1 and the greatest integer less than or equal to .
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