Abstract
ABSTRACT Let be an integral domain and let be a prime ideal of such that every ideal not in is -invertible. We will call such an integral domain a pinched-Krull domain at . In this paper we give some characterizations of a pinched-Krull domain which are analogs of a Krull domain. We also show that is a pinched-Krull domain at if and only if is a pinched-Krull domain at ; and that is a Krull domain if and only if is a pinched-Krull domain at . Let be a nonzero maximal ideal of an integral domain , the natural ring epimorphism, a proper subring of , and . It is proved that if and are Krull domains, then is a pinched-Krull domain at . As an application we give non-Mori domains whose prime -ideals are of finite type. At the end, we study a pinched-Krull domain at a divided prime ideal.
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