Coprimality with a product of integers

The theorem If and are such that is separately coprime with each , then is coprime with their product . The proof Proof: Through B├ęzout. being coprime with each , we can write, for each : If we take the product of each of these expressions, we get: Among the terms of this product, all…

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The composition of polynomials

Definition Let be a commutative field. The polynomials form a commutative unital algebra over containing an element such that the following universal property holds: For any unital algebra (commutative or otherwise) and any element , there exists exactly one unital algebra morphism such that . If and are elements of , let be the unique…

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