Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 149–162

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

Article

DOI: 10.1007/s40306-016-0190-z

Cite this article as:
Phuc, D.V. & Sum, N. Acta Math Vietnam (2017) 42: 149. doi:10.1007/s40306-016-0190-z
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Abstract

Let Pk 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 xi being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for Pk 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 Pk in the case k = 5 and the degree 4(2d−1) with d an arbitrary positive integer.

Keywords

Steenrod squaresPeterson hit problemPolynomial algebra

Mathematics Subject Classification (2010)

55S1055S0555T15

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