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Journal Article

# On the Action of Steenrod Squares on Polynomial Algebras

William M. Singer
Proceedings of the American Mathematical Society
Vol. 111, No. 2 (Feb., 1991), pp. 577-583
DOI: 10.2307/2048351
Stable URL: http://www.jstor.org/stable/2048351
Page Count: 7

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Topics: Algebra, Integers, Mathematical theorems, Polynomials, Abstract algebra, Mathematical problems

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## Abstract

Let Ps be the mod-2 cohomology of the elementary abelian group (Z/2Z) × ⋯ × (Z/2Z) (s factors). The mod-2 Steenrod algebra A acts on Ps according to well-known rules. If $\mathbf{A} \subset A$ denotes the augmentation ideal, then we are interested in determining the image of the action A ⊗ Ps → Ps: the space of elements in Ps that are hit by positive dimensional Steenrod squares. The problem is motivated by applications to cobordism theory [P1] and the homology of the Steenrod algebra [S]. Our main result, which generalizes work of Wood [W], identifies a new class of hit monomials.

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