Ring Theory: We show that polynomial rings over fields are Euclidean domains and explore factorization and extension fields using irreducible polynomials. As an application, we show that the units of a finite field form a cyclic group under multiplication.
Tagged under: mathematics,ring,theory,abstract,algebra,euclidean,domain,integral,principal,ideal,unique,factorization,division,algorithm,field,polynomial,degree,cyclic,finite,abelian,irreducible,prime,extension
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