Polynomial imaginary decompositions for finite separable extensions

• Autorzy: Grygiel A.
• Języki publikacji: EN

Abstrakty

EN

Let K be a field and let L = K[ ξ] be a finite field extension of K of degree m > 1. If ƒ ∈ L[Z] is a polynomial, then there exist unique polynomials uo, ..., um-1 ∈ K[Xo, ...,Xm-i] such that ƒ... [wzór]. A. Nowicki and S. Spodzieja proved that, if K is a field of characteristic zero and ƒ ≠ 0, then uo,..., um-1 have no common divisor in K[Xo,..., Xm-1] of positive degree. We extend this result to the case when L is a separable extension of a field K of arbitrary characteristic. We also show that the same is true for a formal power series in several variables.

Słowa kluczowe

EN

polynomial; decomposition; separable extension

PL

wielomian; rozkład; rozszerzenie rozdzielcze

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 1
• Strony: 9--13
• Opis fizyczny: Bibliogr. 2 poz.

Twórcy

autor

Grygiel A.

• Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland,

Bibliografia

• [1] A. Nowicki and S. Spodzieja, Polynomial imaginary decompositions for finite extensions of fields of characteristic zero, Bull. Polish Acad. Sci. Math. 51 (2003), 157-168.
• [2] A. Schinzel, Polynomials with Special Regard to Reducibility, Cambridge Univ. Press, Cambridge, 2000.