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Regular group algebras whose maximal right and left quotient rings coincide

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1328)

Abstract

We characterize the regular group algebras whose maximal right and left quotient rings coincide. In fact we prove that if K[G] is a regular group algebra, then Qr(K[G]) = Q1(K[G]) if and only if G is abelian-by-finite. This completes the result of Goursaud and Valette, that prove some special cases, namely when K either has positive characteristic or contains all roots of unity.

Keywords

  • Positive Characteristic
  • Group Algebra
  • Group Ring
  • Simple Module
  • Injective Module

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was partially supported by CAICYT grant 3556/83.

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References

  1. F. Cedó, On the maximal quotient ring of regular group rings. To appear in Journal of Algebra.

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  2. D.R. Farkas and R.L. Snider; Group algebras whose simple modules are injective. Trans. A.M.S. 194(1974)241–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. K.R. Goodearl; "Von Neumann regular rings". Pitman. London 1979

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  4. J.-M. Goursaud et J. Valette; Sur l'enveloppe injective des anneaux de groupes réguliers. Bull. Soc. math. France 103(1975)91–102.

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  5. J. Hannah; Countability in regular self-injective rings. Quart. J. Math. Oxford (2) 31(1980)315–327.

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  6. J. Hannah and K.C. O'Meara; Maximal quotient rings of prime group algebras. Proc. A.M.S. 65(1)(1977) 1–7.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. B. Hartley; Injective modules over group rings. Quart. J. Math. Oxford (2)28(1977)1–29.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. D.S. Passman; "The Algebraic Structure of Group Rings". Wiley-Interscience. New York, London 1977.

    MATH  Google Scholar 

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© 1988 Springer-Verlag

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Cedó, F. (1988). Regular group algebras whose maximal right and left quotient rings coincide. In: Bueso, J.L., Jara, P., Torrecillas, B. (eds) Ring Theory. Lecture Notes in Mathematics, vol 1328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100916

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  • DOI: https://doi.org/10.1007/BFb0100916

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19474-3

  • Online ISBN: 978-3-540-39278-1

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