Add to ORKGA, ” namely the condition that every polynomial of the form a0x pn + a1x pn−1 + · · ·+ an−1xp + anx + an+1 with each ai in the residue field k have a root in k, was shown by Whaples to be equivalent to the condition that k have no extensions of degree divisible by p. See the “Afterthought ” to “Maximal Fields with Valuations ” in [Kap95]. Union-closed familie
Let v be a henselian Krull valuation of a field K. In this paper, the authors give some necessary a...
It is known that a finite extension (K′, v′)/(K, v) of discrete valued fields is totally ramified if...
Abstract. Let k be a p-adic field. It is well-known that k has only finitely many extensions of a gi...
namely the condition that every polynomial of the form a0x pn + a1x pn−1 + · · ·+ an−1xp + anx + an...
Abstract. A class of irreducible polynomials P over a valued field (F, v) is introduced, which is th...
This is the fourth part of a four-article series containing a Mizar [3], [2], [1] formalization of K...
Abstract. We classify Artin-Schreier extensions of valued fields with non-trivial defect according t...
Abstract. We classify Artin-Schreier extensions of valued fields with non-trivial defect according t...
This is the first part of a four-article series containing a Mizar [3], [1], [2] formalization of Kr...
This is the second part of a four-article series containing a Mizar [2], [1] formalization of Kronec...
We prove some properties similar to the theorem of Ax-Kochen-Ershov, in some cases of pairs of algeb...
Following Beard, O’Connell and West (1977) we call a polynomial over a finite field Fq perfect if it...
This is the third part of a four-article series containing a Mizar [3], [1], [2] formalization of Kr...
Abstract. Let K be a complete non-archimedean field with a discrete val-uation, f ∈ K[X] a polynomia...
Let v be a henselian Krull valuation of a field K. In this paper, the authors give some necessary a...
Let v be a henselian Krull valuation of a field K. In this paper, the authors give some necessary a...
It is known that a finite extension (K′, v′)/(K, v) of discrete valued fields is totally ramified if...
Abstract. Let k be a p-adic field. It is well-known that k has only finitely many extensions of a gi...
namely the condition that every polynomial of the form a0x pn + a1x pn−1 + · · ·+ an−1xp + anx + an...
Abstract. A class of irreducible polynomials P over a valued field (F, v) is introduced, which is th...
This is the fourth part of a four-article series containing a Mizar [3], [2], [1] formalization of K...
Abstract. We classify Artin-Schreier extensions of valued fields with non-trivial defect according t...
Abstract. We classify Artin-Schreier extensions of valued fields with non-trivial defect according t...
This is the first part of a four-article series containing a Mizar [3], [1], [2] formalization of Kr...
This is the second part of a four-article series containing a Mizar [2], [1] formalization of Kronec...
We prove some properties similar to the theorem of Ax-Kochen-Ershov, in some cases of pairs of algeb...
Following Beard, O’Connell and West (1977) we call a polynomial over a finite field Fq perfect if it...
This is the third part of a four-article series containing a Mizar [3], [1], [2] formalization of Kr...
Abstract. Let K be a complete non-archimedean field with a discrete val-uation, f ∈ K[X] a polynomia...
Let v be a henselian Krull valuation of a field K. In this paper, the authors give some necessary a...
Let v be a henselian Krull valuation of a field K. In this paper, the authors give some necessary a...
It is known that a finite extension (K′, v′)/(K, v) of discrete valued fields is totally ramified if...
Abstract. Let k be a p-adic field. It is well-known that k has only finitely many extensions of a gi...