Mappings of degree 5, part I

• Autorzy: M. Maciejewski , A. Prószyński
• Języki publikacji: EN

Abstrakty

EN

The class of linear (resp. quadratic) mappings over a commutative ring is determined by a set of equation-type relations. For the class of homogeneous polynomial mappings of degree m ≥ 3 it is so over a field, and over a ring there exists a smallest equationally definable class of mappings containing the preceding one. It is proved that generating relations determining that class can be chosen to be strong relations (that is, of the same form over all commutative rings) if{f} m ≤ 5. These relations are already found for m ≤ 4. The purpose of the present paper is to find the first of two parts of generating relations (namely, all the 3-covering relations) satisfied by homogeneous polynomial mappings of degree 5. Moreover, we find some strong (m-2)-relations for any degree m ≥ 4.

Kategorie tematyczne

• 13C13: Other special types
• 11E76: Forms of degree higher than two

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 117
• Numer: 2
• Strony: 223-242

Daty

wydano

2009

Twórcy

autor

M. Maciejewski

• Kazimierz Wielki University, 85-072 Bydgoszcz, Poland

autor

A. Prószyński

• Kazimierz Wielki University, 85-072 Bydgoszcz, Poland

Identyfikatory

DOI

10.4064/cm117-2-5