Sheaf of rings
= Sheaf of rings
= Sheaves of rings
{synonym}
A sheaf of rings assigns a ring $\mathcal O(U)$ to every open set, restriction homomorphisms to inclusions, and satisfies local identity and gluing. It supplies the local functions on a <ringed space>.
This is a ring-valued <Sheaf (mathematics)>, with ring homomorphisms as restriction maps.