On the subalgebra of \(H_*(({\mathbb{R}}\text{P}^\infty)^n;F_2)\) annihilated by Steenrod operations
type: Item
instance of: scholarly article
title: On the subalgebra of \(H_*(({\mathbb{R}}\text{P}^\infty)^n;F_2)\) annihilated by Steenrod operations
zbMATH Open document ID: 0926.55013
DOI: 10.1016/S0022-4049(96)00177-6
published in: Journal of Pure and Applied Algebra
publication date: 1999-11-29T00:00:00Z
review text: Let \(A\) be the mod 2 Steenrod algebra and \(I\) be the augmentation ideal. We denote by \(P(n)= \mathbb{F}_2[x_1, \dots, x_n]\) the polynomial unstable \(A\)-algebra on generators of degree 1. In this paper the authors define a homomorphism \(\theta\) on \(P(n)\) such that \(\theta(I.P(n))=0\). They show that \(\text{Im} \theta\) (or its dual) is related to the problem of finding a basis for \(P(n)/I.P(n)\) [\textit{R. M. W. Wood}, Math. Proc. Camb. Philos. Soc. 105, No. 2, 307-309 (1989; Zbl 0692.55011)].
Mathematics Subject Classification ID: 55S10
zbMATH DE Number: 1308169
zbMATH Keywords: unstable polynomial algebra
zbMATH Keywords: Steenrod algebra
author: Joe Repka
author: Paul Selick
reviewed by: Saïd Zarati
MaRDI profile type: Publication
cites work: Q4010493
cites work: Q4010492
cites work: Steenrod squares of polynomials and the Peterson conjecture
full work available at URL: s0022-4049(96)00177-6
OpenAlex ID: W2095280859
description: scientific article; zbMATH DE number 1308169