The definition of the ring does not explicitly state the operator precedence of the addition and multiplication operators, is this precedence derived from the distributive law?
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5The precedence is a convention, not part of the structure. The convention generally exists to allow for common expressions (such as polynomial expressions) tobe written unambiguously with as few parentheses as possible. They aren't "derived" from anything. – Arturo Magidin Jul 26 '24 at 03:08
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@ArturoMagidin you mean that If I write $a\times b + c$, I default to $(a\times b)+ c$. The explanation works, thanks – 槿铃兔 Jul 26 '24 at 03:32