Certain properties of realizable modules over the Steenrod algebra
type: Item
instance of: scholarly article
title: Certain properties of realizable modules over the Steenrod algebra
zbMATH Open document ID: 0639.55005
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: Let A be the mod p Steenrod algebra. An A module M is said to be realizable if there exists a spectrum X such that \(H^*(X,Z_ p)\cong M\). In the case \(p=2\), \textit{H. R. Margolis} [Bull. Am. Math. Soc. 78, 564-567 (1972; Zbl 0256.55017)] gave a construction for killing the \(P^ s_ t\) homology groups of M in the category of A modules. Since the construction can also be carried out in the category of realizable A modules, if M is realizable then the constructed new module is also realizable; this gives a necessary condition for realizability. In the present paper the author considers the case \(p>2\) and obtains a corresponding result for the element \(P^ 0_ 1\).
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55S10
zbMATH DE Number: 4042841
zbMATH Keywords: realizable module over the Steenrod algebra
zbMATH Keywords: mod p Steenrod algebra
author: Jinkun Lin
reviewed by: K. A. Hardie
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4042841