Integral Overrings of Two-Dimensional Going-Down Domains

Abstract

Abstract.It is proved that if R is a 2-root closed two-dimensional going-down domain with no factor domain of characteristic 2, then each integral overling of R is a going-down domain. An example is given to show that the "2-root closed" hypothesis cannot be deleted.

Characterizations of the Integral Domains Whose Overrings Are Going-Down Domains

“…By applying the classical D + M construction (as in [26]) to such examples, it was shown in [13] that an overring of a going-down domain need not be a going-down domain. In fact, by an iterated pullback construction, it was shown in [19] that an integral overring of a going-down domain need not be a going-down domain. (Earlier, it had been shown that each integral overring of a going-down domain is a going-down domain if dim v (R) ≤ 2 [14] or if R is both locally divided and locally finite-conductor [ [3,Theorem 10].…”