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

Nguyen Khac Tin^1,

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

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

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 , P_k 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 P_k as a graded algebra. Through this isomorphism, we may regard P_k 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.

Keywords:
Steenrod algebra Steenrod polynomial algebra hit problem

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