Invariants of algebraic elements over Henselian fields

On chains associated with abstract key polynomials

“…In the next result we give a connection between saturated distinguished chains and Okutsu frames. It may be pointed that a similar result is also proved in Theorem 2.6 of [13] and Corollary 3.5 of [7] but our proof is elementary.…”

“…The notion of Okutsu frame was introduced by Okutsu in 1982 for local fields [20], and then studied by Nart in [6], which was later generalized to henselian valued field of arbitrary rank in [12] and [13].…”

“…In 1982, Okutsu associated to a monic irreducible polynomial F ∈ K[X] a family of monic irreducible polynomials, F 1 , ..., F r , called the primitive divisor polynomials of F [20], later these polynomials were studied in papers [6], [7], [12] and [13], and they called the chain of such polynomials [F 1 , ..., F r ], an Okutsu frame for F. Moreover, they proved that Okutsu frames, saturated distinguished chains and optimal Maclane chains are closely related. In this paper, we also establish a similar connection between saturated distinguished chains and Okutsu frames, however, our proof is elementary.…”