# Download E-books Rings, Modules, and Algebras in Stable Homotopy Theory (Mathematical Surveys and Monographs) PDF

This booklet introduces a brand new point-set point method of strong homotopy thought that has already had many purposes and gives you to have a long-lasting influence at the topic. Given the sector spectrum $S$, the authors build an associative, commutative, and unital break product in a whole and cocomplete class of ""$S$-modules"" whose derived class is comparable to the classical solid homotopy type. This development permits an easy and algebraically achievable definition of ""$S$-algebras"" and ""commutative $S$-algebras"" by way of associative, or associative and commutative, items $R\wedge SR \longrightarrow R$. those notions are basically such as the sooner notions of $A {\infty$ and $E {\infty$ ring spectra, and the older notions feed clearly into the hot framework to supply abundant examples. there's an both uncomplicated definition of $R$-modules when it comes to maps $R\wedge SM\longrightarrow M$. while $R$ is commutative, the class of $R$-modules additionally has a

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