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Proceedings of the American Mathematical Society

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

 

 

The dimension of the ring of coefficients in a polynomial ring


Author: Jimmy T. Arnold
Journal: Proc. Amer. Math. Soc. 49 (1975), 32-34
DOI: https://doi.org/10.1090/S0002-9939-1975-0360553-4
MathSciNet review: 0360553
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Abstract | References | Additional Information

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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0360553-4
Keywords: Polynomial ring, Krull dimension, coefficient ring
Article copyright: © Copyright 1975 American Mathematical Society