A locally ringed space is a ringed space 
such that every stalk 
is a local
ring. A morphism of locally ringed spaces consists
of a continuous map 
and a compatible morphism 
of sheaves of
rings. Compatibility with restriction maps gives induced stalk
maps 
,
each of which must be a local ring homomorphism.
Every scheme is a locally ringed space. Its sheaf of rings is its structure sheaf.
