On the Structure of the Irreducible Polynomials Over Local Fields Original Research Article

The paper is concerned with the structure of irreducible polynomials in one variable over a local field (K, v). The main achievement is the definition of a system P(ƒ) of invariant factors for each monic irreducible polynomial ƒ set membership, variant K[X]. It is proved that these invariants are characteristic, i.e., by using invariants we may describe the set of irreducible polynomials over a local field.