Integral domains that lose ideals in overrings

William James Heinzer and David C. Lantz

Vol. 145 (1990), No. 2, 223–238

DOI: 10.2140/pjm.1990.145.223

Abstract

We study domains with the property that, in any proper overring, some proper ideal extends to the unit ideal, and domains with the property that, in any proper overring, some proper ideal of a certain type (v-ideal, invertible ideal, or principal ideal) extends to the unit ideal. We characterize the Noetherian domains with these properties, and we show that even the strongest of these properties does not imply the QR-property.

Mathematical Subject Classification 2000

Primary: 13G05

Secondary: 13A15

Milestones

Received: 2 September 1988

Published: 1 October 1990