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Integral domains in which each non-zero ideal is divisorial

Published online by Cambridge University Press:  26 February 2010

William Heinzer
William Heinzer
Affiliation:
Louisiana State University, Baton Rouge, Louisiana.
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Let D be an integral domain with identity having quotient field K. A non-zero fractional ideal F of D is said to be divisorial if F is an intersection of principal fractional ideals of D[4; 2]. Equivalently, F is divisorial if there is a non-zero fractional ideal E of D such that

Divisorial ideals arose in the investigations of Van der Waerden, Artin, and Krull in the 1930's and were called v-ideals by Krull [9; 118]. The concept has played an important role in the development of multiplicative ideal theory.

Type
Research Article
Information
Mathematika , Volume 15 , Issue 2 , December 1968 , pp. 164 - 170
Copyright
Copyright © University College London 1968

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