Highly structured ring spectrum

In mathematics, a highly structured ring spectrum or A ∞ {\displaystyle A_{\infty }} -ring is an object in homotopy theory encoding a refinement of a multiplicative structure on a cohomology theory. A commutative version of an A ∞ {\displaystyle A_{\infty }} -ring is called an E ∞ {\displaystyle E_{\infty }} -ring.