The maximum condition on annihilators for polynomial rings

Cedó, Ferran; Herbera, Dolors

doi:10.1090/S0002-9939-98-04321-4

The maximum condition on annihilators for polynomial rings
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by Ferran Cedó and Dolors Herbera PDF

Proc. Amer. Math. Soc. 126 (1998), 2541-2548 Request permission

Abstract:

For each positive integer $n$, we construct a commutative ring ${\mathcal {R}}$ such that the polynomial ring ${\mathcal {R}}[x_{1},\ldots ,x_{n}]$ satisfies the maximum condition on annihilators and ${\mathcal {R}}[x_{1},\ldots ,x_{n+1}]$ does not. In particular, there exists a commutative Kerr ring ${\mathcal {R}}$ such that ${\mathcal {R}}[x]$ is not Kerr. This answers in the negative a question of Faith’s.

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