For questions on axioms, mathematical statements that are accepted as being true without a mathematical proof.

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What should I be able to do with this chapter on Axiomatic Set Theory in order to check if I've learned it decently? [closed]

I've just read a chapter on axiomatic set theory, from Comprehensive Mathematics for Computer Scientists 1. It comes with basic notation on sets and some axioms: Axiom 1 (Axiom of Empty Set) Axiom 2 ...
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Is it possible to have a field without an additive identity?

If I drop the axiom that Zero is the identity of an addition what consequences does this entail? What do I need to change to my axiomatization? By definition it is not possible, but are there ...