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A characterization of general $ {\rm Z}.{\rm P}.{\rm I}.$-rings


Author: Kathleen B. Levitz
Journal: Proc. Amer. Math. Soc. 32 (1972), 376-380
MSC: Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0294312-5
MathSciNet review: 0294312
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Abstract: A commutative ring A is a general Z.P.I.-ring if each ideal of A can be represented as a finite product of prime ideals. We prove that a commutative ring A is a general Z.P.I.-ring if each finitely generated ideal of A can be represented as a finite product of prime ideals. We also give a characterization of Krull domains in terms of $ ^ \ast $-operations, as defined by Gilmer.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294312-5
Keywords: General Z.P.I.-ring, Dedekind domain, Krull domain, $ ^\ast$-operation, special primary ring
Article copyright: © Copyright 1972 American Mathematical Society