Abstract
It is proved that if R ⊂ T is a minimal ring extension such that (a) the set of zero-divisors of R is contained in a nonmaximal prime ideal of R and (b) each non-zero-divisor of R remains a non-zero-divisor in T, then T is isomorphic to an R-subalgebra of the total quotient ring of R. A nondomain example R ⊂ T satisfying the above hypotheses is given where the Krull dimension of R is any preassigned integer n ≥ 2 and the total quotient ring of R has Krull dimension n − 1. Examples also show that neither of the hypothesis (a), (b) can be deleted. In the case that T is a domain, the above result recovers a theorem of Sato et al. (Citation1992).
2000 Mathematics Subject Classification:
Notes
Communicated by J. Kuzmanovich.