Prime length of crossed products
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- by Charles C. Welsh
- Proc. Amer. Math. Soc. 106 (1989), 91-98
- DOI: https://doi.org/10.1090/S0002-9939-1989-0965248-1
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Abstract:
In this paper we show that the prime length of a crossed product $R*G$, where $R$ is a right Noetherian ring and $G$ is a polycyclic-by-finite group, is bounded by the plinth length of $G$ and the prime length of $R$. We begin by considering prime ideals in group rings of finitely generated Abelian groups, and generalize a theorem of J. E. Roseblade. We then use the description of prime ideals in crossed products given by D. S. Passman to achieve the result.References
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- Donald S. Passman, Group rings of polycyclic groups, Group theory, Academic Press, London, 1984, pp. 207–256. MR 780571
- D. S. Passman, Prime ideals in polycyclic crossed products, Trans. Amer. Math. Soc. 301 (1987), no. 2, 737–759. MR 882713, DOI 10.1090/S0002-9947-1987-0882713-9
- J. E. Roseblade, Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. (3) 36 (1978), no. 3, 385–447. MR 491797, DOI 10.1112/plms/s3-36.3.385
- B. A. F. Wehrfritz, Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76, Springer-Verlag, New York-Heidelberg, 1973. MR 0335656
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 91-98
- MSC: Primary 16A27; Secondary 20C07
- DOI: https://doi.org/10.1090/S0002-9939-1989-0965248-1
- MathSciNet review: 965248