# Rings, Modules, and Algebras in Stable Homotopy Theory

### About this Title

**A. D. Elmendorf**, **I. Kriz**, **M. A. Mandell** and **J. P. May**, with an appendix by **M. Cole**

Publication: Mathematical Surveys and Monographs

Publication Year
1997: Volume 47

ISBNs: 978-0-8218-4303-1 (print); 978-1-4704-1278-4 (online)

DOI: http://dx.doi.org/10.1090/surv/047

MathSciNet review: MR1417719

MSC: Primary 55N20; Secondary 19D10, 19D55, 55P42, 55T25

### Table of Contents

**Front/Back Matter**

**Chapters**

- I. Prologue: the category of $\mathbb {L}$-spectra
- II. Structured ring and module spectra
- III. The homotopy theory of $R$-modules
- IV. The algebraic theory of $R$-modules
- V. $R$-ring spectra and the specialization to $MU$
- VI. Algebraic $K$-theory of $S$-algebras
- VII. $R$-algebras and topological model categories
- VIII. Bousfield localizations of $R$-modules and algebras
- IX. Topological Hochschild homology and cohomology
- X. Some basic constructions on spectra
- XI. Spaces of linear isometries and technical theorems
- XII. The monadic bar construction
- XIII. Epilogue: The category of $\mathbb {L}$-spectra under $S$