I can't seem to figure out the following proposition: Let $A$ be a ring with equal laws of composition, that is, $a+b=ab$ for every $a,\ b \in A$. Show that $A = \{0\}$.
2026-05-15 15:05:34.1778857534
Ring with both laws of composition equal
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$a\in A\implies a=a+0=a(0)=a(a-a)=a^2-a^2=0$