A QUASI-LOCAL HALF-FACTORIAL DOMAIN WITH AN ATOMIC NON-HALF-FACTORIAL INTEGRAL CLOSURE

摘要

We construct a half-factorial quasi-local do-main R, so that its integral closure R = R[t], where t~2, t~3 ∈R, is atomic but not half-factorial; R equals the seminormalization of R. Moreover, R is a quasi-local domain of bounded factorization, and every element in R of zero R-boundary is a unit in R.