Book used: Contemporary Abstract Algebra by Joseph A. Gallian
--2/20/2020--
Read through this article as an introductory text all the way to Galois theory. I will prove that $Q[\alpha]$ is a field, as mentioned in the article. The other axioms of fields are rather trivial here, so I will just do the following two in this post.
--2/14/2020--
I never thought I had to think about polynomial division as much on this problem.
--2/18/2020--
I might have been stuck on this for too long a while. I have a raw idea to expand to the general case but I'm not sure about the details. But I don't want to trap my time in this question- my intention is to get an actual feel of the properties of a field.
--2/20/2020--
Group: a set of elements with one operation: + (additive). Inverse element. Not always commutative.
Ring: two operation. + is communicative & has inverse, * (multiplicative) isn't & no inverse.
Field: two operation, both communicative & has inverse (other than the + identity has no * inverse)
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