Field Theory: We recall basic factoring results for polynomials from Ring Theory and give a definition of a splitting field. This allows one to consider any irreducible polynomial as a set of roots, and in turn we consider when an irreducible polynomial can have multiple roots. We finish with a definition of separable elements and extensions.
Tagged under: mathematics,abstract,algbera,field,theory,ring,polynomial,root,extension,algebraic,separable,Euclidean,domain,finite,characteristic,prime,irreducible,unique,factorization,multiplicity
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