Difficult))) Every finite integral domain is a field. This concept never did sink in previously, but as I read the details of theorem 5.10 it did. Also that the number of elements of fields {Zp[x]/(p(x))} is p-raised to the degree of p(x).
F is a subfield of F[x]/p(x). F[x]/p(x) also called an extension field of F and if p(x) is irreducible in F[x] then p(x) has a root in F[x]/p(x).
Eventhough p(x) is irreducible in F[x] it may be reducible in F[x]/p(x). In fact
From there, it all kind of fell apart in a heap of confusion. How does multiplication work, and addition, and how does C relate to R[x]/x^2 +1?
I have lots of questions and I need to see lots more examples before I find consolation in this section
Reflective)))
This section shows us how complex number systems were established and became common use.
It helps us solidify when F[x]/p(x) is a field (therefore an integral domain).
We learn a vocabulary word of the extension field.
And there is a relation defined for a root of an irreducible p(x) in a field extension.
I am looking for teacher to provide further examples of application for the theorems in this section.
This concept was harder fro me to graps than any other.
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