Noetherian rings with free additive groups

O’Neill, John D.

doi:10.1090/S0002-9939-1984-0759643-9

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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Noetherian rings with free additive groups
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by John D. O’Neill PDF

Proc. Amer. Math. Soc. 92 (1984), 323-324 Request permission

Abstract:

There exists a Noetherian ring of arbitrarily large cardinality with free additive group. This answers a problem of L. Fuchs.

References

László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
John D. O’Neill, An uncountable Noetherian ring with free additive group, Proc. Amer. Math. Soc. 66 (1977), no. 2, 205–207. MR 450426, DOI 10.1090/S0002-9939-1977-0450426-2