Suppose that $G$ is an Abelian group and $A$ and $B$ are both direct summands of $G$, i.e. there exist subgroups $C$ and $D$ such that $G=A\oplus C = B\oplus D$. Then my question is, under what conditions is $A\oplus B$ a direct summand of $G$? Does it suffice that $A\cap B = 0$, and if not what more is required?
2026-03-31 07:08:49.1774940929
Are direct summands of an Abelian group always direct summands together?
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