Suppose $A,B$ abelian groups, such that $A\oplus B\approx A$, can I conclude that $B=0$?
If it's true, is there any hint how to prove it?
2026-03-27 07:14:29.1774595669
If $A\oplus B\approx A$ then $B=0$?
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No; consider $A=\Bbb{Z}^{\Bbb{N}}=\bigoplus_{n\in\Bbb{N}}\Bbb{Z}$.