Question about distributive law in definition of a ring – math.stackexchange.com

Question about distributive law in definition of a ring – math.stackexchange.com

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In the definition of a ring $R$, one has $a(b+c) = ab + ac$ and $(a+b)c = ac + bc$ for all $a,b,c\in R$ My question is (just out of curiosity) if one really needs both of these. I can't think of ...

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