Multiplicative structures on bordism spectra

Construction 10.2.25 (Multiplicative structures on bordism spectra). Let \(B\) be a commutative monoid in animae and let \[ \phi \colon B\longrightarrow \BOP \] be a morphism of commutative monoids. Since the J-homomorphism is symmetric monoidal, so is the composite \[ B\xrightarrow {\phi }\BOP \xrightarrow {J}\Pic (\S )\subseteq \Sp . \] Consequently, Construction 10.2.8 equips \(MB\) with a canonical commutative ring spectrum structure.