Fundamentals on Nostr: The identity is the number "e" that - when you use the operation with any element "a" ...

The identity is the number "e" that - when you use the operation with any element "a" (a o e, a + e if the operation is addition) you get a as a result. That is why the additive identity is zero.

A field does have to be closed under both addition and multiplication, but it also needs more, like commutativity, and units under multiplication as well as being an integral domain (not having zero divisors) among other things.