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Seems tautological to talk about a proper subset that is not equal to the set. Call it a subset, and then state that it is not equal.
- A ring needs a 'one' element as it is otherwise just a 'RNG'. - Also the leading coefficient must be non zero, thus the zero polynomial has no degree. - Some typos
Algebra I: Commutative Rings. Commutative Rings. Replace "1 \neq 0" with "nontrivial", and add remark about convention of degree of zero polynomial. Fix typo