Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On Arnold's formula for the dimension of a polynomial ring


Author: Paul Eakin
Journal: Proc. Amer. Math. Soc. 54 (1976), 11-15
MathSciNet review: 0387270
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Abstract: If $ R$ is a commutative integral domain with quotient field $ K$ and $ {x_1}, \ldots ,{x_n}$ are indeterminates, then there exist $ {\theta _1}, \ldots ,{\theta _n}$ in $ K$ such that $ \dim R[{x_1}, \ldots ,{x_n}] = n + \dim R[{\theta _1}, \ldots ,{\theta _n}]$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0387270-X
Keywords: Krull dimension, polynomial ring
Article copyright: © Copyright 1976 American Mathematical Society