Science/Engineering Rings, Modules, and Algebras in Stable Homotopy Theory (Mathematical Surveys & Monographs) (0821843036)

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Rings, Modules, and Algebras in Stable Homotopy Theory (Mathematical Surveys & Monographs)

This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of "$S$-modules" whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of "$S$-algebras" and "commutative $S$-algebras" in terms of associative, or associative and commutative, products $R\wedge _SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A_{\infty }$ and $E_{\infty }$ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge _SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has an associative, commutative, and unital smash product, and its derived category has properties just like the stable homotopy category. These constructions allow the importation into stable homotopy theory of a great deal of point-set level algebra.

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	Science/Engineering Algebras, Rings And Their Representations: Proceedings Of The International Conference on Algebras, Modules and Rings, Lisbon, Catarina Santa-Clara “Algebras, Rings And Their Representations: Proceedings Of The International Conference on Algebras, Modules and Rings, Lisbon, Portugal, 14-18 July 2003" World Scientific Publishing Company \| 2006-02-20 \| ISBN: 9812 ...
	*Science/Engineering Crossed Products of C^ Algebras (Mathematical Surveys and Monographs)** Crossed Products of C^* Algebras (Mathematical Surveys and Monographs)American Mathematical Society \| ISBN: 0821842420 \| 2007-02-20 \| PDF \| 528 pages \| 3 Mb The theory of crossed products is extremely rich and intriguing. There are applicat ...
	Study Algebraic Methods in Unstable Homotopy Theory (New Mathematical Monographs) Joseph Neisendorfer "Algebraic Methods in Unstable Homotopy Theory (New Mathematical Monographs)"Cambridge University Press \| English \| 2009-12-31 \| ISBN: 0521760372 \| 552 pages \| PDF \| 1,6 MBThe most modern and thorough treatment of unstab ...
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	Study Invariant Theory of Finite Groups (Mathematical Surveys and Monographs) Mara D. Neusel, Larry Smith "Invariant Theory of Finite Groups (Mathematical Surveys and Monographs)"American Mathematical Society \| English \| 2001-12-04 \| ISBN: 0821829165 \| 371 pages \| DJVU \| 11 MBThe questions that have been at the cente ...
	Rings, Modules, and Algebras in Stable Homotopy Theory A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, M. Cole, "Rings, Modules, and Algebras in Stable Homotopy Theory" American Mathematical Society \| 2007 \| ISBN: 0821843036 \| 249 pages \| Djvu \| 3,1 MB This book introduces a new point-s ...

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