We construct a free and transitive action of the group of bilinear forms on the set of –products on , a regular quotient of an even –ring spectrum with . We show that this action induces a free and transitive action of the group of quadratic forms on the set of equivalence classes of –products on . The characteristic bilinear form of introduced by the authors in a previous paper is the natural obstruction to commutativity of . We discuss the examples of the Morava –theories and the –periodic Morava –theories .
"Quadratic forms classify products on quotient ring spectra." Algebr. Geom. Topol. 12 (3) 1405 - 1441, 2012. https://doi.org/10.2140/agt.2012.12.1405