A ring which is a domain locally but not globally

Roitman, Moshe

doi:10.1090/S0002-9939-1985-0773990-7

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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A ring which is a domain locally but not globally
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by Moshe Roitman

Proc. Amer. Math. Soc. 93 (1985), 409-410

DOI: https://doi.org/10.1090/S0002-9939-1985-0773990-7

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Abstract:

We present here a connected commutative ring $R$ which is not a domain, but ${R_P}$ is a domain for any prime ideal $P$ of $R$.

References

Anthony V. Geramita and Charles Small, Introduction to homological methods in commutative rings, Queen’s Papers in Pure and Applied Mathematics, No. 43, Queen’s University, Kingston, Ont., 1976. MR 0417146