Some counterexamples related to integral closure in 𝐷[[𝑥]]

Abstract

JACK OHM(i) 0. Introduction. This investigation arose from the recent discovery that an integral domain D may be integrally closed without the power series ring -D [[x]] being integrally closed, which is a consequence (by considering, for example, a valuation ring of rank > 1) of the following theorem : 0.1 Theorem ([1-a, p. 76, Exercise 27], [17]). Let D be an integrally closed domain. Then D[[x]] integrally closed implies f~\fL0alD = Ofor every nonunit a eD(2).