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Ring spectrum : ウィキペディア英語版
Ring spectrum

In stable homotopy theory, a ring spectrum is a spectrum ''E'' together with a multiplication map
:''μ'':''E'' ∧ ''E'' → ''E''
and a unit map
: ''η'':''S'' → ''E'',
where ''S'' is the sphere spectrum. These maps have to satisfy associativity and unitality conditions up to homotopy much in the same way as the multiplication of a ring is associative and unital. That is,
: ''μ'' (id ∧ ''μ'') ∼ ''μ'' (''μ'' ∧ id)
and
: ''μ'' (id ∧ ''η'') ∼ id ∼ ''μ''(''η'' ∧ id).
Examples of ring spectra include singular homology with coefficients in a ring, complex cobordism, K-theory, and Morava K-theory.
== See also ==

*Highly structured ring spectrum

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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