Multiplications on cohomology theories with coefficients

Abstract

Araki and Toda have considered the existence and classification of multiplications on generalized cohomology theories with coefficients in the category of finite CW-complexes. We consider the same matters for representable cohomology theories in a category of stable CW-spectra, such as that constructed by Adams. We obtain similar, and in certain instances stronger, results than Araki and Toda, with methods of proof that are often simpler and more straightforward.