John wrote:
>And finally, if you make \\(\mathbb{Z}/2\\) into a *ring* with both addition and multiplication as its operations, mathematicians often call it \\(\mathbb{F}_2\\)

So here what was meant is "**field**", not "**ring**" (although field is a ring, of course), or this is another subtlety which I'm missing - for some reason John emphasized the word *ring*.