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Proceedings of the American Mathematical Society

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

 

 

Constructive aspects of Noetherian rings


Author: Fred Richman
Journal: Proc. Amer. Math. Soc. 44 (1974), 436-441
MSC: Primary 02E99; Secondary 13E05
MathSciNet review: 0416874
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Abstract: If $ R$ is a discrete Noetherian ring, in the sense of Tennenbaum, such that finitely generated ideals are finitely related and detachable, then so is $ R[x]$. This shows that a large class of rings enjoy the property that finitely generated ideals are detachable, and that intersections and quotients of finitely generated ideals are finitely generated.


References [Enhancements On Off] (What's this?)

  • [1] J. B. Tennenbaum, A constructive version of Hilbert's basis theorem, Ph.D. Dissertation, University of California, San Diego, Calif., 1973.

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DOI: https://doi.org/10.1090/S0002-9939-1974-0416874-9
Article copyright: © Copyright 1974 American Mathematical Society