Six notes on chains of prime ideals

Summary The following topics are considered: saturated chains of prime ideals in quadratic (resp., simple, local, and level) integral extension domains of a local domain R; the heights of a prime ideal and its contraction in integral extension domains of R; and, the nonexistence of intermediate rings between R and finite integral extension domains of R that are minimal with spect to having certain properties.Research on this paper was supported in part by the National Science Foundation, Grant MCS 8001597.