The global dimension of FBN rings with enough clans

Damiano, Robert F.

doi:10.1090/S0002-9939-1982-0663859-8

The global dimension of FBN rings with enough clans
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by Robert F. Damiano

Proc. Amer. Math. Soc. 86 (1982), 25-28

DOI: https://doi.org/10.1090/S0002-9939-1982-0663859-8

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Abstract:

For an FBN ring $R$, a classical set of prime ideals $\left \{ {{P_1}, \ldots ,{P_n}} \right \}$ is one for which the semiprime ideal $N = \cap _{i = 1}^n{P_i}$ satisfies the Artin-Rees property. A minimal classical set is called a clan. We say an FBN ring $R$ has enough clans if each prime ideal $P$ is an element of a clan. In this paper, we show that for such rings the Krull dimension is less than or equal to the global dimension.

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