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  text: 'A field is a [3gq commutative ring] $(R, +, \\times)$ (henceforth abbreviated simply as $R$, with multiplicative identity $1$ and additive identity $0$) which additionally has the property that every nonzero element has a multiplicative inverse: for every $r \\in R$ there is $x \\in R$ such that $xr = rx = 1$.\nConventionally we insist that a field must have more than one element: equivalently, $0 \\not = 1$.\n\n# Examples\n\n<work in progress>',
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