I think the most important things we've learned so far are the theorems involving modular arithmetic, especially those concerning solving modular algebra equations, and the concepts of isomorphism and homomorphism along with the axioms of showing whether two rings are isomorphic or homomorphic.
I imagine that the test will mostly include equations to solve in modular arithmetic and potential rings to test and figure out if they have identity or are commutative or integral domains or fields or isomorphic to another ring.
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