Agreement of the Eilenberg–MacLane constructions

Remark 8.3.6 (Agreement of the Eilenberg–MacLane constructions). For an ordinary associative \(R\)-algebra \(A\), the ring spectrum \(H_R(A[0])\) is canonically equivalent to the direct Eilenberg–MacLane ring spectrum \(HA\) from Corollary 8.3.1. Indeed, both are concentrated in degree \(0\), and their multiplications induce the ordinary multiplication of \(A\) on \(\pi _0\). The classification of associative ring spectra concentrated in degree \(0\) from Corollary 14.5.4 therefore identifies them. If \(A\) is commutative, the same argument gives an equivalence of commutative ring spectra.