Jaffard ring

In mathematics, a Jaffard ring is a type of ring, more general than a Noetherian ring. Formally, a Jaffard ring is a ring "R" such that

:$dim\; R\; [T]\; =\; 1\; +\; dim\; R,\; ,$

where "dim" denotes Krull dimension. A Jaffard ring that is also an integral domain is called a Jaffard domain.

The Jaffard property is satisfied by any Noetherian ring "R", so examples of non-Jaffardian rings are quite difficult to find. Nonetheless, an example was given in 1953 by Abraham Seidenberg: the subring of

:$overline\{mathbf\{QT$

consisting of those formal power series whose constant term is rational.

References

* cite journal
last = Seidenberg
first = Abraham
authorlink = Abraham Seidenberg
title = A note on the dimension theory of rings
journal = Pacific J. Math.
volume = 3
year = 1953
pages = 505–512
issn = 0030-8730 MathSciNet|id=0054571

External links

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