Abstract Algebra | Irreducible polynomials

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We introduce the notion of an irreducible polynomial over the ring k[x] where k is any field. A proof that p(x) is irreducible if and only if (p(x)) is maximal is also given, along with some examples.

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So glad to find your channel. I just bought an abstract algebra book and was looking through a proof in the section "Irreducible Polynomials Are Maximal Ideals" and thought I'd type that "section title" into Youtube to see what would come up...and here you are. I'm looking forward to watching more of your stuff.

maxdominate
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You can try to prove it yourself and skip ahead to 8:47 to watch the applications.

maxdickens
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Brother you are doing great work..Love from India 🇮🇳🇮🇳🇮🇳

rac
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Does this proof extend to the multi variable case ?

keyblade