Discussion of the multiplicative identity in rings

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created: 2022-02-16 14:41:39
modified: 2022-02-16 14:49:19

When considering the mathematical objects called rings, the following identity for the multiplicative identity is an optional axiom:

There is no approved consensus if we should use this identity or not, but there are several points against/in line with it:

Yes No
It makes things easier Even integers satisfy other axioms, but do not have this identity
Easy to add an identity to an existing ring, without complicating things too much continuous functions (see smoothness) with compact support cannot have an identity, since the 1 constant function is not compact