D-NICE POLYNOMIALS WITH FOUR ROOTS OVER INTEGRAL DOMAINS D OF ANY CHARACTERISTIC

Jonathan GROVES

Makale detayları

D-NICE POLYNOMIALS WITH FOUR ROOTS OVER INTEGRAL DOMAINS D OF ANY CHARACTERISTIC

Yazarlar:

Jonathan GROVES

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2009 Vol.5 Issue 5, pp.78-105

Belge Tipi:

Makale

Yayın Tarihi:

5/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000718410

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

Let D be an integral domain of any characteristic. We say that p(x) ∈ D[x] is D-nice if p(x) and its derivative p0(x) split in D[x]. We begin by presenting a new equivalence relation for D-nice polynomials over integral domains D of characteristic p > 0, which leads to an important modification of our definition of equivalence classes of D-nice polynomials. We then present a partial solution to the unsolved problem of constructing and counting equivalence classes of D-nice polynomials p(x) with four distinct roots. We consider the following three cases separately: (1) D has characteristic 0, (2) D has characteristic p > 0 and the degree of p(x) is not a multiple of p, and (3) D has characteristic p > 0 and the degree of p(x) is a multiple of p. In all these cases we give formulas for constructing some examples. In the final case we also count equivalence classes of D-nice polynomials for certain choices of the multiplicities of the roots of p(x). To conclude, we state several problems about D-nice polynomials with four roots that remain unsolved.

Makale detayları

D-NICE POLYNOMIALS WITH FOUR ROOTS OVER INTEGRAL DOMAINS D OF ANY CHARACTERISTIC

Yazarlar: Jonathan GROVES

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2009 Vol.5 Issue 5, pp.78-105

Belge Tipi: Makale

Yayın Tarihi: 5/2009

Belge Dili: Türkçe

Document ID (Org No.): 2000718410

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

Jonathan GROVES

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2009 Vol.5 Issue 5, pp.78-105

Belge Tipi:

Makale

Yayın Tarihi:

5/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000718410

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048