Soient l'algèbre de Steenrod mod-2 et l'algèbre polynomiale graduée à k générateurs sur le corps à deux éléments , chaque générateur étant de degré 1. Nous étudions le problème suivant soulevé par F. Peterson : déterminer un système minimal de générateurs comme module sur l'algèbre de Steenrod pour , problème appelé hit problem en anglais. Dans ce but, nous étudions le hit problem en degré , avec . Cette solution implique un résultat de Mothebe [4,5].
Let be the polynomial algebra over the prime field of two elements, , in k variables , each of degree 1. We are interested in the Peterson hit problem of finding a minimal set of generators for as a module over the mod-2 Steenrod algebra, . In this paper, we study the hit problem in degree , with d a positive integer. Our result implies the one of Mothebe [4,5].
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@article{CRMATH_2015__353_11_1035_0, author = {V\~o Ph\'uc, {\DJ}ặng and Sum, Nguyễn}, title = {On the generators of the polynomial algebra as a module over the {Steenrod} algebra}, journal = {Comptes Rendus. Math\'ematique}, pages = {1035--1040}, publisher = {Elsevier}, volume = {353}, number = {11}, year = {2015}, doi = {10.1016/j.crma.2015.09.002}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.09.002/} }
TY - JOUR AU - Võ Phúc, Đặng AU - Sum, Nguyễn TI - On the generators of the polynomial algebra as a module over the Steenrod algebra JO - Comptes Rendus. Mathématique PY - 2015 SP - 1035 EP - 1040 VL - 353 IS - 11 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2015.09.002/ DO - 10.1016/j.crma.2015.09.002 LA - en ID - CRMATH_2015__353_11_1035_0 ER -
%0 Journal Article %A Võ Phúc, Đặng %A Sum, Nguyễn %T On the generators of the polynomial algebra as a module over the Steenrod algebra %J Comptes Rendus. Mathématique %D 2015 %P 1035-1040 %V 353 %N 11 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2015.09.002/ %R 10.1016/j.crma.2015.09.002 %G en %F CRMATH_2015__353_11_1035_0
Võ Phúc, Đặng; Sum, Nguyễn. On the generators of the polynomial algebra as a module over the Steenrod algebra. Comptes Rendus. Mathématique, Tome 353 (2015) no. 11, pp. 1035-1040. doi : 10.1016/j.crma.2015.09.002. http://archive.numdam.org/articles/10.1016/j.crma.2015.09.002/
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