On Arnold’s formula for the dimension of a polynomial ring
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- by Paul Eakin PDF
- Proc. Amer. Math. Soc. 54 (1976), 11-15 Request permission
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 $\dim R[{x_1}, \ldots ,{x_n}] = n + \dim R[{\theta _1}, \ldots ,{\theta _n}]$.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 11-15
- DOI: https://doi.org/10.1090/S0002-9939-1976-0387270-X
- MathSciNet review: 0387270