Mappings of degree 5, part I

M. Maciejewski, and A. Prószyński. "Mappings of degree 5, part I." Colloquium Mathematicae 117.2 (2009): 223-242. <http://eudml.org/doc/284292>.

@article{M2009,
abstract = {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.},
author = {M. Maciejewski, A. Prószyński},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {223-242},
title = {Mappings of degree 5, part I},
url = {http://eudml.org/doc/284292},
volume = {117},
year = {2009},
}

TY - JOUR
AU - M. Maciejewski
AU - A. Prószyński
TI - Mappings of degree 5, part I
JO - Colloquium Mathematicae
PY - 2009
VL - 117
IS - 2
SP - 223
EP - 242
AB - 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.
LA - eng
UR - http://eudml.org/doc/284292
ER -