The OSPF domain (also called an AS) is the collection of OSPF areas connected to the OSPF backbone.
RFC 2328, OSPF Version 2 defines the term, Router ID:"
A 32-bit number assigned to each router running the OSPF
protocol. This number uniquely identifies the router within
an Autonomous System.
A 32-bit number that uniquely identifies this router in the AS.
One possible implementation strategy would be to use the
smallest IP interface address belonging to the router. If a
router's OSPF Router ID is changed, the router's OSPF software
should be restarted before the new Router ID takes effect. In
this case the router should flush its self-originated LSAs from
the routing domain (see Section 14.1) before restarting, or they
will persist for up to MaxAge minutes.