Rings, Modules, and Algebras in Stable Homotopy Theory
	Категория: Естественные науки » Физико-математические науки » Математика, геометрия, статистика
		Автор: A.D.Elmendorf, I.Kriz, M.A.Mandell, J.P.May Издательство: American Mathematical Society Год издания: 1997 isbn: 0821806386 Количество страниц: 260 Язык: english Формат: DJVU Размер: 3 Мб Каталожный номер: 38945	It is tempting to refer to (commutative) S-algebras as (commutative) ring spectra. However, this would introduce confusion since the term "ring spectrum" has had a definite meaning for thirty years as a stable homotopy category level notion. Ring spectra in the classical homotopical sense are not rendered obsolete by our theory since there are many examples that admit no S-algebra structure. In any case, the term S-algebra more accurately describes our new concept. With our theory, and the new possibilities that it opens up, it becomes vitally important to keep track of when one is working on the point-set level and when one is working up to homotopy. In the absence (or ignorance) of a good point-set level category of spectra, topologists have tended to be sloppy about this.
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