Rings Modules and Algebras in Stable Homotopy Theory is popular PDF and ePub book, written by Anthony D. Elmendorf in 1997, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Rings Modules and Algebras in Stable Homotopy Theory can be Read Online from any device for your convenience.
Rings Modules and Algebras in Stable Homotopy Theory Book PDF Summary
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 a
Detail Book of Rings Modules and Algebras in Stable Homotopy Theory PDF
- Author : Anthony D. Elmendorf
- Release : 30 September 1997
- Publisher : American Mathematical Soc.
- ISBN : 9780821843031
- Genre : Mathematics
- Total Page : 265 pages
- Language : English
- PDF File Size : 15,7 Mb
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