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 🔴 Abstract Algebra Exam 1 Review Problems and Solutions:    • Abstract Algebra Exam 1 Review Problems an...   🔴 Abstract Algebra Exam 2 Review Problems and Solutions:    • Abstract Algebra Exam 2 Review Problems an...   🔴 Abstract Algebra Exam 3 Review Problems and Solutions:    • Abstract Algebra Exam 3 Review Problems an...   🔴 Abstract Algebra Final Exam Review Problems and Solutions:    • Abstract Algebra Final Exam Review Problem...   🔴 Abstract Algebra Problems with Solutions (including Proofs):    • Abstract Algebra Problems with Solutions (...   🔴 Abstract Algebra Lectures Playlist:    • Abstract Algebra Course, Lecture 1: Introd...   🔴 Check out my blog at: https://infinityisreallybig.com/ #RingTheory #AbstractAlgebra Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / billkinneymath   🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ 🔴 Desiring God website: https://www.desiringgod.org/ AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.