
The paper under review gives a characterization of the rings with finitely many minimal prime ideals: Let \(R\) be a commutative ring with identity. Then \(\mathrm{Min}(R)\) is finite if and only if for any \(\mathfrak{p} \in \mathrm{Min}(R)\), there exists a finitely generated ideal \(\mathfrak{p}^*\) of \(R\) such that \(\mathfrak{p}^* \subseteq \mathfrak{p}\) and \(\mathrm{Min}(R/\mathfrak{p}^*)\) is finite. This result is an extension of results in [\textit{D. D. Anderson}, Proc. Am. Math. Soc. 122, No. 1, 13--14 (1994; Zbl 0841.13001)] and [\textit{R. Gilmer} and \textit{W. Heinzer}, Manuscr. Math. 78, No. 2, 201--221 (1993; Zbl 0794.13002)].
radical, minimal prime ideal, Ideals and multiplicative ideal theory in commutative rings
radical, minimal prime ideal, Ideals and multiplicative ideal theory in commutative rings
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