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http://dx.doi.org/10.4134/CKMS.c190076

${\mathfrak{A}}$-GENERATORS FOR THE POLYNOMIAL ALGEBRA OF FIVE VARIABLES IN DEGREE 5(2t - 1) + 6 · 2t  

Phuc, Dang Vo (Faculty of Education Studies University of Khanh Hoa)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 371-399 More about this Journal
Abstract
Let Ps := 𝔽2[x1, x2, …, xs] = ⊕n⩾0(Ps)n be the polynomial algebra viewed as a graded left module over the mod 2 Steenrod algebra, ${\mathfrak{A}}$. The grading is by the degree of the homogeneous terms (Ps)n of degree n in the variables x1, x2, …, xs of grading 1. We are interested in the hit problem, set up by F. P. Peterson, of finding a minimal system of generators for ${\mathfrak{A}}$-module Ps. Equivalently, we want to find a basis for the 𝔽2-graded vector space ${\mathbb{F}}_2{\otimes}_{\mathfrak{A}}$ Ps. In this paper, we study the hit problem in the case s = 5 and the degree n = 5(2t - 1) + 6 · 2t with t an arbitrary positive integer.
Keywords
Steenrod squares; Peterson hit problem; polynomial algebra;
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