A two-dimensional non-Noetherian factorial ring

Gilmer, Robert

doi:10.1090/S0002-9939-1974-0335500-0

A two-dimensional non-Noetherian factorial ring
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Proc. Amer. Math. Soc. 44 (1974), 25-30 Request permission

Abstract:

Let $R$ be a commutative ring with identity and let $G$ be an abelian group of torsion-free rank $\alpha$. If $\{ {X_\lambda }\}$ is a set of indeterminates over $R$ of cardinality $\alpha$, then the group ring of $G$ over $R$ and the polynomial ring $R[\{ {X_\lambda }\} ]$ have the same (Krull) dimension. The preceding result and a theorem due to T. Parker and the author imply that for each integer $k \geqq 2$, there is a $k$-dimensional non-Noetherian unique factorization domain of arbitrary characteristic.

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Some non-Noetherian factorial rings

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