So I'm a bit confused with this... I'm learning some field theory and I've just learnt about groups of units. With rings this makes sense. However say $F$ is a field then isn't every element in $F$ besides the additive identity (call it $0$) a unit by definition? I mean in a field every element has a multiplicative inverse... So wouldn't the group of units in $F$ just be everything besides $0$. I know we talk about this with respect to finite field.. but I mean wouldn't the same logic apply?
2026-03-28 17:40:17.1774719617
Group of units of a field
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