A commutative ring spectrum, in the homotopy-category convention, satisfies , where interchanges the factors of the smash product of spectra. This condition alone does not assert an refinement.
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In the context of stable homotopy theory, a **commutative ring spectrum** is a type of spectrum that captures both the combinatorial aspects of algebra and the topological aspects of stable homotopy theory. ### Basic Concepts 1. **Spectrum**: A spectrum is a sequence of spaces (or pointed topological spaces) that are connected by stable homotopy equivalences.