show that $(\mathbb Z\oplus \mathbb Z)/(m\mathbb Z\oplus n\mathbb Z) \cong \mathbb Z_n\oplus \mathbb Z_m$ using the first isomorphic theorm i don't know how actually but the question ordered the proof of that $(\oplus )/(I\oplus J) ≈ R/I\oplus S/J$ first and let us base on it to prove the first line
2026-03-26 22:57:52.1774565872
Show that $(\mathbb Z\oplus \mathbb Z)/(m\mathbb Z\oplus n\mathbb Z) \cong \mathbb Z_n\oplus \mathbb Z_m$
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