Simplicial commutative ring

In algebra, a simplicial commutative ring is a commutative monoid in the category of simplicial abelian groups, or, equivalently, a simplicial object in the category of commutative rings. If A is a simplicial commutative ring, then it can be shown that π 0 A {\displaystyle \pi _{0}A} is a ring and π i A {\displaystyle \pi _{i}A} are modules over that ring (in fact, π ∗ A {\displaystyle \pi _{*}A} is a graded ring over π 0 A {\displaystyle \pi _{0}A} .) A topology-counterpart of this notion is a commutative ring spectrum.

Source: Wikipedia — Simplicial commutative ring (CC BY-SA 4.0)