LOCALLY HENSELIAN GOING-DOWN DOMAINS

For an integral domain R, several necessary and sufficient conditions are given for R to be unibranched inside its absolute integral closure ; one such condition is that np be Henselian for each prime ideal P of R. Additional conditions are given in case R is a going-down domain. Unlike the situation in the Noetherian context, such going-down domain s R need not be quasilocal or of Krull dimension at most 1. A number o f examples are given for the locally pseudo-valuation domain case.