Stafford, J. T. Dimensions of division rings. (English) Zbl 0517.16014 Isr. J. Math. 45, 33-40 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 6 Documents MSC: 16Kxx Division rings and semisimple Artin rings 16P60 Chain conditions on annihilators and summands: Goldie-type conditions 16E10 Homological dimension in associative algebras 16S34 Group rings 17B35 Universal enveloping (super)algebras Keywords:torsion-free polycyclic-by-finite group; quotient division ring; group algebra; Hirsch number; Krull dimension; global homological dimension; enveloping algebras; finite-dimensional Lie algebra; augmentation ideals; Gel’fand-Kirillov conjecture Citations:Zbl 0425.16013; Zbl 0468.17003 PDFBibTeX XMLCite \textit{J. T. Stafford}, Isr. J. Math. 45, 33--40 (1983; Zbl 0517.16014) Full Text: DOI References: [1] Cartan, H.; Eilenberg, S., Homological Algebra (1956), Princeton: Princeton Univ. Press, Princeton · Zbl 0075.24305 [2] Clift, G. H., Zero divisors and idempotents in group rings, Can. J. Math., 32, 596-602 (1980) · Zbl 0439.16011 [3] Dixmier, J., Enveloping Algebras (1977), Amsterdam: North-Holland, Amsterdam · Zbl 0366.17007 [4] Eilenberg, S.; Rosenberg, A.; Zelinsky, D., On the dimension of modules and algebras, VII, Nagoya J. Math., 12, 71-93 (1957) · Zbl 0212.05901 [5] Fel’dman, G. L., On the homological dimension of solvable groups, Math. USSR—Izv., 5, 1231-1244 (1971) · Zbl 0252.18017 · doi:10.1070/IM1971v005n06ABEH001231 [6] Moeglin, C., Ideaux primitifs des algèbres enveloppantes, J. Math. Pures Appl., 59, 265-336 (1980) · Zbl 0454.17006 [7] Rentschler, R.; Gabriel, P., Sur la dimension des anneaux et ensembles ordonnés, C. R. Acad. Sci. Paris (A), 265, 712-715 (1967) · Zbl 0155.36201 [8] Resco, R. D., Krull dimension of Noetherian algebras and extensions of the base field, Commun. Algebra, 8, 161-183 (1980) · Zbl 0425.16013 · doi:10.1080/00927878008822452 [9] Resco, R. D., A dimension theorem for division rings, Isr. J. Math., 35, 215-221 (1980) · Zbl 0437.16014 · doi:10.1007/BF02761192 [10] Rosenberg, A., Homological dimension and transcendence degree, Commun. Algebra, 10, 329-338 (1982) · Zbl 0481.16007 · doi:10.1080/00927878208822718 [11] Rotman, J. J., An Introduction to Homological Algebra (1979), New York: Academic Press, New York · Zbl 0441.18018 [12] Smith, P. F., On the dimension of group rings: Corrigendum, Proc. Lond. Math. Soc., 25, 288-302 (1972) · Zbl 0236.16011 · doi:10.1112/plms/s3-25.2.288 [13] Smith, S. P., The Krull dimension of the enveloping algebra of sl(2,C), J. Algebra, 71, 189-194 (1981) · Zbl 0468.17003 · doi:10.1016/0021-8693(81)90114-9 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.