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A note on the Krull dimension of certain algebras

Part of: Division rings and semisimple Artin rings

Published online by Cambridge University Press:  26 February 2010

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London. El 4NS
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Abstract. For F a field we compute, explicitly and directly, the right Krull dimension of the algebra Qop⊗FQ for certain semisimple Artinian F-algebras Q. (Here Qop denotes the opposite ring of Q.) We use our calculation to give alternative proofs of some theorems of J. T. Stafford and A. I. Lichtman. Our methods involve a detailed study of skew polynomial rings.

MSC classification

Secondary: 16K20: Finite-dimensional
Type
Research Article
Information
Mathematika , Volume 39 , Issue 1 , June 1992 , pp. 49 - 55
Copyright
Copyright © University College London 1992

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References

1.Bell, A. D.. When are all prime ideals in an Ore extension Goldie? Comm. in Algebra, 13 (1985), 1743–1762.CrossRefGoogle Scholar
2.Chatters, A. W. and Hajarnavis, C. R.. Rings with Chain Conditions (Pitman, Londonetc., 1980).Google Scholar
3.Lichtman, A. I.. The Tits alternative for linear groups over rings of fractions of polycyclic group rings. Preprint, 1990.Google Scholar
4.McConnell, J. C. and Robson, J. C.. Non-commutative Noetherian Rings (John Wiley & Sons, Chichester etc., 1987).Google Scholar
5.Resco, R.. Transcendental division algebras and simple Noetherian rings. Israel J. Math., 32 (1979), 236–256.CrossRefGoogle Scholar
6.Shirvani, M. and Wehrfritz, B. A. F.. Skew Linear Groups (Cambridge Univ. Press, Cambridge etc., 1986).Google Scholar
7.Stafford, J. T.. Dimensions of division rings. Israel J. Math., 45 (1983), 33–40.CrossRefGoogle Scholar