# Rings, modules, and algebras in stable homotopy theory by A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, and M.

By A. D. Elmendorf, I. Kriz, M. A. Mandell, J. P. May, and M. Cole

This ebook introduces a brand new point-set point method of solid homotopy thought that has already had many purposes and gives you to have an enduring effect at the topic. Given the field spectrum $S$, the authors build an associative, commutative, and unital spoil product in an entire and cocomplete class of ""$S$-modules"" whose derived class is similar to the classical reliable homotopy type. This development permits an easy and algebraically achievable definition of ""$S$-algebras"" and ""commutative $S$-algebras"" when it comes to associative, or associative and commutative, items $R\wedge SR \longrightarrow R$. those notions are primarily such as the sooner notions of $A {\infty$ and $E {\infty$ ring spectra, and the older notions feed certainly into the recent 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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Extra resources for Rings, modules, and algebras in stable homotopy theory

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5 If n > 1, then 3 2n-. 5. 526753 . . ; in particular, F(n) > 4az" for n > 1. The proof of this is omitted. References [1] X. M. Chang, F. K. Hwang and J. F. Weng, Group testing with two and three defectives, Ann. N. Y. Acad. Sci. Vol. 576, Ed. M. F. Capobianco, M. Guan, D. F. Hsu and F. Tian, (New York, 1989) 86-96. [2] R. Dorfman, The detection of defective members of large populations, Ann. Math. Statist. 14 (1943) 436-440. [3] M. C. Hu, F. K. Hwang and J. K. Wang, A boundary problem for group testing, SIAM J.

F. Capobianco, M. Guan, D. F. Hsu and F. Tian, (New York, 1989) 86-96. [2] R. Dorfman, The detection of defective members of large populations, Ann. Math. Statist. 14 (1943) 436-440. [3] M. C. Hu, F. K. Hwang and J. K. Wang, A boundary problem for group testing, SIAM J. AIg. Disc. Methods 2 (1981) 81-87. [4] F. K. Hwang, A minimax procedure on group testing problems, Tamkang J. Math. 2 (1971) 39-44. [5] F. K. Hwang, Hypergeometric group testing procedures and merging procedures, Bull. Inst. Math.

1, S -a S1 --^ S implies n S1 = S n {D1} # 0. This implies D1 E S n So. Since D1 ¢ S, S n So S. (iii) = (i): Trivially true by using the definition of realizability. 3 Li ' s s-Stage Algorithm Li [12] extended a 2-stage algorithm of Dorfman [2] (for PGT) to s stages . At stage 1 the n items are arbitrarily divided into gl groups of k, ( some possibly k, - 1) items. Each of these groups is tested and items in pure groups are identified as good and removed. Items in contaminated groups are pooled together and arbitrarily redivided into g2 groups of k2 (some possibly k2 - 1) items; thus entering stage 2.