Hong, Chan Yong; Kim, Hong Kee; Park, Jae Keol Rings with restricted descending chain conditions. (English) Zbl 0882.16015 Commun. Algebra 25, No. 8, 2579-2584 (1997). The authors prove that if \(R\) is a ring all of whose left primitive factor rings are Artinian and \(R\) satisfies the descending chain condition on essential left ideals then every prime ideal of \(R\) is maximal and \(R\) is strongly \(\pi\)-regular. Applications to PI-rings are given. Reviewer: Xue Weimin (Fouzhou) Cited in 2 Documents MSC: 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) 16D25 Ideals in associative algebras Keywords:PI-rings; strongly \(\pi\)-regular rings; left primitive factor rings; descending chain condition on essential left ideals; prime ideals PDFBibTeX XMLCite \textit{C. Y. Hong} et al., Commun. Algebra 25, No. 8, 2579--2584 (1997; Zbl 0882.16015) Full Text: DOI References: [1] DOI: 10.1080/00927878008822460 · Zbl 0444.16015 · doi:10.1080/00927878008822460 [2] DOI: 10.1080/00927877808822263 · Zbl 0383.16014 · doi:10.1080/00927877808822263 [3] DOI: 10.1090/S0002-9939-1994-1231028-7 · doi:10.1090/S0002-9939-1994-1231028-7 [4] DOI: 10.1016/0021-8693(79)90174-1 · Zbl 0411.16015 · doi:10.1016/0021-8693(79)90174-1 [5] Dischinger F., C. R Acad. Sci. 283 pp 571– (1976) [6] DOI: 10.1007/BF01277059 · Zbl 0658.16018 · doi:10.1007/BF01277059 [7] Fisher J.W., Pacific J. Math. 54 pp 135– (1974) [8] Goodearl K.R., Von Neumann Regular Rings (1979) [9] DOI: 10.1090/S0002-9904-1948-09049-8 · Zbl 0032.00701 · doi:10.1090/S0002-9904-1948-09049-8 [10] DOI: 10.1090/S0002-9939-1960-0111765-5 · doi:10.1090/S0002-9939-1960-0111765-5 [11] Procesi C., Rings with Polynomial Identity (1973) · Zbl 0262.16018 [12] DOI: 10.1017/S0017089500030342 · Zbl 0819.16001 · doi:10.1017/S0017089500030342 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.