×

Division algebras generated by finitely generated nilpotent groups. (English) Zbl 0527.16008


MSC:

16S34 Group rings
16Kxx Division rings and semisimple Artin rings
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
16U60 Units, groups of units (associative rings and algebras)
20C07 Group rings of infinite groups and their modules (group-theoretic aspects)
20F18 Nilpotent groups
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bergman, G. M., Historical addendum, 2, 2, 41-42 (1979) · Zbl 0409.16001
[2] Borho, W.; Gabriel, P.; Rentschler, R., Primideale in Einhüllenden auflösbarer Lie-Algebren (1973), Springer: Springer Berlin/Heidelberg/New York · Zbl 0293.17005
[3] Farkas, D. R.; Schofield, A. H.; Snider, R. L.; Stafford, J. T., The isomorphism question for division rings of group rings, (Proc. Amer. Math. Soc., 85 (1982)), 327-330 · Zbl 0495.16006
[4] Fields, D. E., Zero divisors and nilpotent elements in power series rings, (Proc. Amer. Math. Soc., 27 (1971)), 427-433 · Zbl 0219.13023
[5] Hilbert, D., Grundlagen der Geometrie (1899), Teubner: Teubner Leipzig · JFM 30.0424.01
[6] Levi-Civita, T., Sugli infiniti ed infinitesimi attulai quali elementi analitici, Atti 1st. Veneto Sci. Lett. Arti, IV, VII, 1765-1815 (1892-1893)
[7] Lorenz, M., Primitive ideals in crossed products and rings with finite group actions, Math. Z., 158, 285-294 (1978) · Zbl 0356.16013
[8] Lorenz, M.; Passman, D. S., Prime ideals in crossed products of finite groups, Israel J. Math., 33, 89-132 (1979) · Zbl 0426.16008
[9] Malcev, A. I., On embedding of group algebras in a division algebra, Dokl. Akad. Nauk SSSR, 60, 1499-1501 (1948), [Russian] · Zbl 0034.30901
[10] Neumann, B. H., On ordered division rings, Trans. Amer. Math. Soc., 66, 202-252 (1949) · Zbl 0035.30401
[11] Passman, D. S., The Algebraic Structure of Group Rings (1977), Wiley-Interscience: Wiley-Interscience New York · Zbl 0366.16003
[12] Schilling, O. F.G, Noncommutative valuations, Bull. Amer. Math. Soc., 51, 297-304 (1945) · Zbl 0061.05601
[13] Zalesskii, A. E., Irreducible representations of finitely generated nilpotent torsion-free groups, Math. Notes, 9, 117-123 (1971)
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.