Field Theory: We consider the case of simple extensions, where we adjoin a single element to a given field. The cases of transcendental and algebraic arise, depending on whether the kernel of the evaluation map is zero or not. In the algebraic case, we define the minimal polynomial, show it is irreducible, and calculate the degree of the extension.
Tagged under: mathematics,field,theory,ring,abstract algebra,extension,simple,subfield,algebraic,transcendental,homomorphism,kernel,ideal,evaluation,maximal,Euclidean,domain,principal,unique,factorization,irreducible,Ring (mathematics)
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