9 October 2012
4:00 - 5:00   M Barr

On the limit closure of domains


This is a new exposition of an old theorem of Kennison's that characterizes the limit closure of integral domains inside the category of commutative rings. A ring in the limit closure must obviously be a subobject of a product of domains (they are called semi-prime rings and characterized by the absence of non-zero nilpotents), but not all such rings are in the limit closure. Rings in the limit closure are characterized by the fact that any element (1) that is a square mod every prime and (2) whose cube is a square, is iself a square. They are also characterized as global sections of a sheaf of domains. For any commutative ring R, the ring of global sections of a certain sheaf of integral domains is the coreflector of R into the limit closure of domains.