Nonuniqueness of coefficient rings in a polynomial ring

Hochster, M.

doi:10.1090/S0002-9939-1972-0294325-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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Nonuniqueness of coefficient rings in a polynomial ring
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by M. Hochster PDF

Proc. Amer. Math. Soc. 34 (1972), 81-82 Request permission

Abstract:

An example is given of commutative rings B, C with 1 such that $B\ncong C$ but $B[t] \cong C[t]$, where t is an indeterminate.

References

Shreeram S. Abhyankar, William Heinzer, and Paul Eakin, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310–342. MR 306173, DOI 10.1016/0021-8693(72)90134-2

Polynomial invariance of rings

Paul Eakin and K. K. Kubota, A note on the uniqueness of rings of coefficients in polynomial rings, Proc. Amer. Math. Soc. 32 (1972), 333–341. MR 297763, DOI 10.1090/S0002-9939-1972-0297763-8