The rank of abelian groups with commutative endomorphism ring.

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 Q G is flat as a Q E (G) -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 n 2 4 + 1 . [ABSTRACT FROM AUTHOR]