On the hit problem for the polynomial algebra

Nguyễn Sum

doi:10.1016/j.crma.2013.07.016

Topology

On the hit problem for the polynomial algebra
[Sur le hit problem pour lʼalgèbre polynomiale]

Présenté par : the Editorial Board

Nguyễn Sum ¹

¹ Department of Mathematics, Quy Nhơn University, 170 An Dương Vương, Quy Nhơn, Bi`nh Định, Viet Nam

Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 565-568.

Résumé
Abstract

Nous étudions le problème suivant soulevé par F. Peterson : déterminer un système minimal de générateurs comme module sur lʼalgèbre de Steenrod pour lʼalgèbre polynomiale $P_{k} : = F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ , problème appelé hit problem en anglais. Dans ce but, nous étudions un ensemble minimal de générateurs pour le $A$ -module $P_{k}$ dans certains degrés dits génériques. En appliquant ces résultats, nous déterminons explicitement le hit problem pour $k = 4$ .

We study the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra $P_{k} : = F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ as a module over the mod-2 Steenrod algebra, $A$ . In this Note, we study a minimal set of generators for $A$ -module $P_{k}$ in some so-called generic degrees and apply these results to explicitly determine the hit problem for $k = 4$ .

Reçu le : 2013-06-04
Accepté le : 2013-07-17
Publié le : 2013-07-01

DOI : 10.1016/j.crma.2013.07.016

Affiliations des auteurs :

Nguyễn Sum ¹

¹ Department of Mathematics, Quy Nhơn University, 170 An Dương Vương, Quy Nhơn, Bi`nh Định, Viet Nam

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Nguyễn Sum. On the hit problem for the polynomial algebra. Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 565-568. doi : 10.1016/j.crma.2013.07.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.016/

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Cité par

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Cité par Sources :

^☆ The work was supported in part by a grant of NAFOSTED.

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