1) So can you basically consider an associate to be something that is divisible by a certain polynomial? And according to my understanding, it also means that if a=bu, then b=au^-1. In the definition for irreducible polynomials, is it suggesting that some polynomials are divisible by anything? I guess I can't really see the difference between "associates" and just being divisible by something else or reducible.
2) Do irreducible polynomials sort of act like primes in certain ways? Or do we sort of consider "associates" to be like a prime factorization of a polynomial?
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