The dimension of the ring of coefficients in a polynomial ring

Arnold, Jimmy T.

doi:10.1090/S0002-9939-1975-0360553-4

The dimension of the ring of coefficients in a polynomial ring
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by Jimmy T. Arnold PDF

Proc. Amer. Math. Soc. 49 (1975), 32-34 Request permission

Abstract:

$A$ and $B$ are commutative rings with identity. We say that $A$ and $B$ are stably equivalent provided there exists a positive integer $n$ such that the polynomial rings $A[{X_1}, \cdots ,{X_n}]$ and $B[{Y_1}, \cdots ,{Y_n}]$ are isomorphic. If $A$ and $B$ are stably equivalent, then they have equal Krull dimension.

References

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Additional Information

Journal: Proc. Amer. Math. Soc. 49 (1975), 32-34
DOI: https://doi.org/10.1090/S0002-9939-1975-0360553-4
MathSciNet review: 0360553