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The Laskerian property, power series rings and Noetherian spectra


Authors: Robert Gilmer and William Heinzer
Journal: Proc. Amer. Math. Soc. 79 (1980), 13-16
MSC: Primary 13E05; Secondary 13J05
DOI: https://doi.org/10.1090/S0002-9939-1980-0560575-6
MathSciNet review: 560575
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Abstract: We show that if the power series ring $ R[[X]]$ in one indeterminate over a commutative ring R with identity is Laskerian, then R is Noetherian. On the other hand, if $ R[[X]]$ is a ZD-ring, then R has Noetherian spectrum, but R need not be Noetherian. We show that, in general, a Laskerian ring has Noetherian spectrum.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0560575-6
Keywords: Laskerian ring, power series ring, Noetherian, ZD-ring, Noetherian spectrum
Article copyright: © Copyright 1980 American Mathematical Society

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