Journal of Mathematical Sciences and Applications
ISSN (Print): 2333-8784 ISSN (Online): 2333-8792 Website: Editor-in-chief: Prof. (Dr.) Vishwa Nath Maurya, Cenap ozel
Open Access
Journal Browser
Journal of Mathematical Sciences and Applications. 2014, 2(2), 21-24
DOI: 10.12691/jmsa-2-2-2
Open AccessArticle

The Admissible Monomial Basis for the Polynomial Algebra of Five Variables in Degree Eight

Nguyen Khac Tin1,

1Foundation Sciences Faculty, University of Technical Education of Ho Chi Minh city, Viet Nam

Pub. Date: April 23, 2014

Cite this paper:
Nguyen Khac Tin. The Admissible Monomial Basis for the Polynomial Algebra of Five Variables in Degree Eight. Journal of Mathematical Sciences and Applications. 2014; 2(2):21-24. doi: 10.12691/jmsa-2-2-2


We study the hit problem, set up by F. Peterson of finding a minimal set of generators for the polynomial algebra as a module over the mod-2 Steenrod algebra, A. By assigning degree 1 to each , Pk is regarded as a graded algebra over the ground field F2. The mod 2 cohomology ring of the k-fold Cartesian product of infinite dimensional real projective spaces is isomorphic to Pk as a graded algebra. Through this isomorphism, we may regard Pk as an A-module where A stands for the mod 2 Steenrod algebra. In this paper, we explicitly determine the hit problem for the case of k=5 in degree 8 in terms of the admissible monomials.

Steenrod algebra Steenrod polynomial algebra hit problem

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  N. H. V. Hung, The cohomology of the Steenrod algebra and representations of the generalinear groups, Trans. Amer. Math. Soc. 357(2005), 4065-4089.
[2]  M. Kameko, Products of projective spaces as Steenrod modules, Thesis Johns Hopkins University, 1990.
[3]  T. N. Nam, A-générateurs génériquess pour l’algèbre polynomiale, Adv. Math. 186(2004), 334-362.
[4]  F. P. Peterson, Generators of H*(RP × RP) as a module over the Steenrod algebra, Abstracts Amer. Math. Soc. No.833 April 1987.
[5]  S. Priddy, On characterizing summands in the classifying space of a group, I,Amer. Jour. Math. 112(1990), 737-748.
[6]  J. H. Silverman, Hit polynomials and the canonical antimonomorphism of the Steenrod algebra, Proc.Amer.Math.Soc. 123(1995), 627-637. The transfer in homological algebra, Math.Zeit, 202 (1989), 493-523.
[7]  W. M. Singer, On the action of the Steenrod squares on polynomial algebras, Proc. Amer. Math. Soc. 111(1991), 577-583.
[8]  N. E. Steenrod, Cohomology operations, Lectures by N. E. Steenrod written and revised by D. B. A. Epstein, Annals of Mathematics, No.50, Princeton University Press, Princeton N.J(1962).
[9]  N. Sum, The negative answer to Kameko’s conjecture on the hit problem, Advances in Mathematics,(2010) 225:5, 2365-2390.
[10]  N. Sum, On the Peterson hit problem, preprint, 2013, 59pages (submitted).
[11]  N. Sum, On the hit problem for the polynomial algebra, C. R. Math. Acad. Sci. Pari, Ser. I, 351 ( 2013), 565-568.
[12]  G. Walker and R. M. W. Wood, Young tableaux and the Steenrod algebra, Proceedings of the International School and Conferenca in Algebraic Topology, Ha Noi 2004, Geom.Topol. Monogr., Geom.Topol. Publ.,Coventry 11(2007), 379-397.