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W. M. Singer, On the action of the Steenrod squares on polynomial algebras, Proc. Amer. Math. Soc. 111(1991), 577-583.

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Article

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

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


Journal of Mathematical Sciences and Applications. 2014, Vol. 2 No. 2, 21-24
DOI: 10.12691/jmsa-2-2-2
Copyright © 2014 Science and Education Publishing

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.

Correspondence to: Nguyen  Khac Tin, Foundation Sciences Faculty, University of Technical Education of Ho Chi Minh city, Viet Nam. Email: tinnk@hcmute.edu.vn

Abstract

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.

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