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Dimensions of division rings. (English) Zbl 0517.16014


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
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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
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[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
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[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
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