Eilenberg–MacLane ring spectra of DGAs

Definition 8.3.5 (Eilenberg–MacLane ring spectrum). Let \(A\) be an associative DGA over a commutative ring \(R\). Its Eilenberg–MacLane ring spectrum is the associative ring spectrum \[ HA:=H_R(\gamma A)\in \Alg (\Sp ). \] If \(A\) is a commutative DGA, the lax symmetric monoidal structure on \(H_R\circ \gamma \) refines \(HA\) to a commutative ring spectrum.