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Factoring Ideals into Semiprime Ideals

Published online by Cambridge University Press:  20 November 2018

N. H. Vaughan  and
R. W. Yeagy
N. H. Vaughan
Affiliation:
Stephen F. Austin State University, Nacogdoches, Texas
R. W. Yeagy
Affiliation:
Stephen F. Austin State University, Nacogdoches, Texas
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Let D be an integral domain with 1 ≠ 0 . We consider “property SP” in D, which is that every ideal is a product of semiprime ideals. (A semiprime ideal is equal to its radical.) It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. We prove that a domain D with property SP is almost Dedekind, and we give an example of a nonnoetherian almost Dedekind domain with property SP.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1313 - 1318
Copyright
Copyright © Canadian Mathematical Society 1978

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