THE v-OPERATION IN EXTENSIONS OF INTEGRAL DOMAINS

Abstract

An extension D ⊆ R of integral domains is strongly t-compatible (respectively, t-compatible) if (IR)-1 = (I-1R)v (respectively, (IR)v = (IvR)v) for every nonzero finitely generated fractional ideal I of D. We show that strongly t-compatible implies t-compatible and give examples to show that the converse does not hold. We also indicate situations where strong t-compatibility and its variants show up naturally. In addition, we study integral domains D such that D ⊆ R is strongly t-compatible (respectively, t-compatible) for every overring R of D.