Overrings of commutative rings. I. Noetherian overrings

Abstract

In this paper: "ring" means commutative ring with unit; a subring must always have the same identity element as the ring of which it is a subring; "dimension" (of a ring) means Krull dimension (the supremum of the lengths of all chains of prime ideals in the ring) ; ring T is an overring of ring R if R is a subring of T, and T is a sub-ring of the total quotient ring of R.