Sigurdsson, Gunnar Differential operator rings whose prime factors have bounded Goldie dimension. (English) Zbl 0522.16003 Arch. Math. 42, 348-353 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 15 Documents MSC: 16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras) 16P60 Chain conditions on annihilators and summands: Goldie-type conditions 16W20 Automorphisms and endomorphisms 16P40 Noetherian rings and modules (associative rings and algebras) 17B35 Universal enveloping (super)algebras 17B30 Solvable, nilpotent (super)algebras Keywords:universal enveloping algebra of finite dimensional solvable Lie algebra; differential operator ring; right Noetherian ring; Goldie dimension of prime factors; completely prime PDF BibTeX XML Cite \textit{G. Sigurdsson}, Arch. Math. 42, 348--353 (1984; Zbl 0522.16003) Full Text: DOI References: [1] A. D.Bell, Goldie dimension of prime factors of polynomial and skew polynomial rings. To appear. · Zbl 0522.16004 [2] W.Borho, P.Gabriel and R.Rentschler, Primideale in Einhüllenden auflösbarer Lie-Algebren. LNM357, Berlin-Heidelberg-New York 1973. · Zbl 0293.17005 [3] J.Cozzens and C.Faith, Simple Noetherian rings. Cambridge 1975. · Zbl 0314.16001 [4] J.Dixmier, Enveloping algebras. Amsterdam-New York-Oxford 1977. · Zbl 0346.17010 [5] K. R. Goodearl andR. B. Warfield, Krull dimension of differential operator rings. Proc. London Math. Soc. (3),45, 49-70 (1982). · Zbl 0493.16004 · doi:10.1112/plms/s3-45.1.49 [6] K. R. Goodearl andR. B. Warfield, Primitivity in differential operator rings. Math. Z.180, 503-523 (1982). · Zbl 0495.16002 · doi:10.1007/BF01214722 [7] R.Gordon and J. C.Robson, Krull dimension. Mem. Amer. Math. Soc.133, Providence, R.I. 1973. · Zbl 0269.16017 [8] D. A. Jordan, Noetherian Ore extensions and Jacobson rings. J. London Math. Soc. (2),10, 281-291 (1975). · Zbl 0313.16011 · doi:10.1112/jlms/s2-10.3.281 [9] M. Lorenz, Completely prime ideals in Ore extensions. Comm. Algebra,9 (11), 1227-1232 (1981). · Zbl 0464.16001 · doi:10.1080/00927878108822642 [10] P. Revoy, Algebres de Weyl en characteristiquep. C. Rend. Acad. Sc. Paris276, 225-228 (1973). [11] J. T. Stafford, Generating modules efficiently: algebraicK-Xheory for non-commutative Noetherian rings. J. Algebra69, 312-346 (1981). · Zbl 0456.16026 · doi:10.1016/0021-8693(81)90208-8 [12] J. T. Stafford, Homological properties of the enveloping algebraU(SL 2). Math. Proc. Cambridge Phil. Soc.91, 29-37 (1982). · Zbl 0478.17006 · doi:10.1017/S0305004100059089 [13] P. Vamos, On the minimal prime ideals of a tensor product of two fields. Math. Proc. Cambridge Phil. Soc.84, 23-35 (1978). · Zbl 0404.12017 · doi:10.1017/S0305004100054840 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.