Abstract Algebra 15.4: Irreducible Polynomials
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5 жыл бұрынWhen working in polynomial rings over an integral domain, polynomials can be either reducible or irreducible. We begin to discuss some of the consequences of this.
@priyamhazarika2744 Жыл бұрын
Thank you 😊, it was helpful and time saving
@Forced2 4 жыл бұрын
Amazing video.
@patrickjones1510 4 жыл бұрын
Thank you. I created these videos for an online class that I was teaching, and I'm always happy that other people find them useful.
@bobonaqa 2 жыл бұрын
am more confused than before haha... but don't worry, it's probably just me
@sangeethag1408 3 жыл бұрын
Prove that Any polynomial in F[x] can be written in a unique manner as a product of irreducible polynomials in F[x] , can you give a proof for this question?
@patrickjones4813 3 жыл бұрын
The basic idea, which you'll have to add details to, is that suppose f(x) is a polynomial is F[x]. It is either reducible, or irreducible. If it is irreducible, you're done. If it is reducible, then it factors into polynomials of lower degree than the original. Those polynomials are individually either reducible or irreducible. Repeat the original argument. Because the degrees have to be lower each step, this can't be an infinite process.
@sangeethag1408 3 жыл бұрын
@@patrickjones4813 Thank you sir
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