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Highly structured ring spectrum
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<p>In mathematics, a highly structured ring spectrum or A ∞ {\displaystyle A_{\infty }} -ring is an object in <a href="/facts/Homotopy_theory/MJwYyRny">homotopy theory</a> encoding a refinement of a multiplicative structure on a <a href="/facts/Cohomology_theory/J7FJzTNh">cohomology theory</a>. A commutative version of an A ∞ {\displaystyle A_{\infty }} -ring is called an E ∞ {\displaystyle E_{\infty }} -ring. While originally motivated by questions of <a href="/facts/Geometric_topology/NpsqSK2N">geometric topology</a> and <a href="/facts/Fibre_bundle/SJ7Ek6cI">bundle theory</a>, they are today most often used in <a href="/facts/Stable_homotopy_theory/wnedyf7K">stable homotopy theory</a>. </p>