Irreducibility Over the Rationals.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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A brief historical survey indicates the type of general irreducibility criteria that are sufficient for irreducibility over the rationals. Three general approaches to the problem are then examined in turn. The first of these involves an application of ideal theory for number fields, the second a construction of Newton polygons for which an appropriate multiplication theorem holds and the last a method for constructing non-Archimedean values on the field of fractions of the ring of polynomials over the rationals from which irreducibility criteria can be deduced. The conclusion summarizes the nature of these attempts.
- Theoretical Mathematics