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Trying to read that is like trying to learn an entire new language by reading a sentence in it. Way too many words to already understand what it's even defining (commutative ring, irreducible polynomials, UFDs, principle ideal, nozero prime ideal... and I'm not following why p divides ab in R... or even exactly what that means).

Searching youtube kahn academy and numberphile, but not turning up anything. exactly how high level is this?

This is usually part of an introductory undergrad course in algebra. What you're looking for is called "ring theory".

Michael Artin's Algebra is a good, concrete book with tons of motivation and zero prerequisites. Wanna try it? ;)

I'm currently taking a course on this material in 2nd year undergrad.

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