Naghipour, A. R. A short note on minimal prime ideals. (English) Zbl 1303.13001 J. Commut. Algebra 6, No. 2, 231-232 (2014). 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 [D. D. Anderson, Proc. Am. Math. Soc. 122, No. 1, 13–14 (1994; Zbl 0841.13001)] and [R. Gilmer and W. Heinzer, Manuscr. Math. 78, No. 2, 201–221 (1993; Zbl 0794.13002)]. Reviewer: Truong Thi Hong Thanh (Hanoi) Cited in 2 Documents MSC: 13A15 Ideals and multiplicative ideal theory in commutative rings Keywords:minimal prime ideal; radical Citations:Zbl 0841.13001; Zbl 0794.13002 × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] D.D. Anderson, A note on minimal prime ideals , Proc. Amer. Math. Soc. 122 (1994), 13-14. · Zbl 0841.13001 · doi:10.2307/2160834 [2] R. Gilmer and W. Heinzer, Primary ideals with finitely generated radical in a commutative ring , Manuscr. Math. 78 (1993), 201-221. · Zbl 0794.13002 · doi:10.1007/BF02599309 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.