Stable homotopy over the Steenrod algebra (Q2718317)

In [Axiomatic stable homotopy theory, Mem. Am. Math. Soc. 610 (1997; Zbl 0881.55001)], \textit{M. Hovey}, \textit{J. H. Palmieri} and \textit{N. P. Strickland} introduced the notion of `stable homotopy category', giving a suitable setting in which to try and do stable homotopy theory in an algebraic fashion. In the work under review, the author uses this to present a unified approach to a number of results about the Steenrod algebra which are analogues of results in homotopy theory.NEWLINENEWLINENEWLINEEverything is done in a certain category of `modules' (actually comodules over the dual Steenrod algebra), where the trivial module \({\mathbb F}_{p}\) plays the role of the sphere spectrum, and \(\text{ Ext}\) plays the role of homotopy classes of maps.NEWLINENEWLINENEWLINEThe author's stated aims are to provide a single source for a number of results on the Steenrod algebra and to give an example of the use of axiomatic stable homotopy theory. He succeeds admirably on both counts.