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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Krull dimension in power series rings


Author: Jimmy T. Arnold
Journal: Trans. Amer. Math. Soc. 177 (1973), 299-304
MSC: Primary 13J05
MathSciNet review: 0316451
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Abstract: Let R denote a commutative ring with identity. If there exists a chain $ {P_0} \subset {P_1} \subset \cdots \subset {P_n}$ of $ n + 1$ prime ideals of R, where $ {P_n} \ne R$, but no such chain of $ n + 2$ prime ideals, then we say that R has dimension n. The power series ring $ R[[X]]$ may have infinite dimension even though R has finite dimension.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0316451-8
Keywords: Dimension, power series ring
Article copyright: © Copyright 1973 American Mathematical Society