×

A dimension theorem for division rings. (English) Zbl 0437.16014


MSC:

16Kxx Division rings and semisimple Artin rings
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16E10 Homological dimension in associative algebras
Full Text: DOI

References:

[1] Amitsur, S. A.; Small, L. W., Polynomials over division rings, Israel J. Math., 31, 353-358 (1978) · Zbl 0395.16013
[2] Bhatwadekar, S., On the global dimension of some filtered algebras, J. London Math. Soc., 13, 2, 239-248 (1976) · Zbl 0332.16012 · doi:10.1112/jlms/s2-13.2.239
[3] Kaplansky, I., Fields and Rings (1969), Chicago: University of Chicago Press, Chicago
[4] Passman, D. S., The Algebraic Structure of Group Rings (1977), New York-London: John Wiley and Sons, New York-London · Zbl 0368.16003
[5] Rentschler, R.; Gabriel, P., Sur la dimension des anneaux et ensembles ordonnes, C. R. Acad. Sci Paris Ser. A, 265, 712-715 (1967) · Zbl 0155.36201
[6] Resco, R., Transcendental division algebras and simple Noetherian rings, Israel J. Math., 32, 236-256 (1979) · Zbl 0404.16012
[7] Rinehart, G. S.; Rosenberg, A.; Tierney, M., The global dimension of Ore extensions and Weyl algebras, Algebra, Topology, and Category Theory, 169-180 (1976), New York: Academic Press, New York · Zbl 0336.16028
[8] Rosenberg, A.; Stafford, J. T.; Tierney, M., Global dimension of Ore extensions, Algebra, Topology, and Category Theory, 181-188 (1976), New York: Academic Press, New York · Zbl 0336.16029
[9] Smith, P. F., On the intersection theorem, Proc. London Math. Soc., 21, 3, 385-398 (1970) · doi:10.1112/plms/s3-21.3.385
[10] Stenström, B., Rings of Quotients (1975), Berlin-New York: Springer-Verlag, Berlin-New York · Zbl 0296.16001
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.