Rings Can Be Strange in Abstract Algebra

In Ring Theory from Abstract Algebra, what is the definition of a ring? The ring does not have to be commutative or contain a unity. Sometimes the unity doesn't have to be "1" ({0,2,4} is a subring of ℤ6 with unity but its unity is "4"!!!). Proving basic properties of rings can be tricky. Polynomial rings like ℤ2[x] will be our main emphasis. Fields and integral domains are the nicest rings (no zero divisors). 🔴 "Contemporary Abstract Algebra", by Joe Gallian: https://amzn.to/2ZqLc1J

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