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Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 149–162 | Cite as

On a Minimal Set of Generators for the Polynomial Algebra of Five Variables as a Module over the Steenrod Algebra

  • Dang Vo Phuc
  • Nguyen Sum
Article
  • 99 Downloads

Abstract

Let P k be the graded polynomial algebra \(\mathbb {F}_{2}[x_{1},x_{2},{\ldots } ,x_{k}]\) over the prime field of two elements, \(\mathbb {F}_{2}\), with the degree of each x i being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for P k as a module over the mod-2 Steenrod algebra, \(\mathcal {A}\). In this paper, we explicitly determine a minimal set of \(\mathcal {A}\)-generators for P k in the case k = 5 and the degree 4(2 d −1) with d an arbitrary positive integer.

Keywords

Steenrod squares Peterson hit problem Polynomial algebra 

Mathematics Subject Classification (2010)

55S10 55S05 55T15 

Notes

Acknowledgments

The final version of this paper was completed while the second named author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM) from August to December 2015. He would like to thank the VIASM for financial support and kind hospitality. The work was supported in part by a grant of the NAFOSTED.

We would like to express our warmest thanks to the referee for the careful reading and helpful suggestions.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of MathematicsQuy Nhon UniversityBinh DinhVietnam

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