Difficult:
The material was so intuitive that it was hard to follow the formalisms of the proofs. It is also unintuitive why Lemma 3.25 was proven, while reducibility holding over the obvious homomorphism from Z[t] to Zn[t] was left unproven. Along those lines, the general sloppiness of the proofs in this book are hurting the formal parts of my brain, as I tend to be similarly sloppy with my first draft proofs, so I'm not getting as good of a feel for the formalisms of the material.
Reflective:
The fact that irreducibility in Zn[t] implies irreducibility in Z[t], is quite a useful fact. if f in Zn[t] is irreducible, then any g in Z[t] that maps to f in Zn[t] is irreducible, and the number of g's that fit that criterion for a given f are infinite. Countable, assuming degree(g) < infinity, but still infinite. Also, I noticed that by that criterion, a similar criterion exists to the Eisenstein criterion. If f(t) in Z[t] = sigma(an*f^n) and m|an for all n except m does not divide a0, then f maps to g in Zm[t] where g = a0, which is irreducible.
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