Skip to main content

Class groups of orders and a mayer-vietoris sequence

  • 377 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 353)

Keywords

  • Class Group
  • Picard Group
  • Algebraic Number Theory
  • Algebraic Number Field
  • Ideal Class Group

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 is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Bass, Algebraic K-theory, Math. Lecture Note Series, Benjamin, New York, 1968.

    MATH  Google Scholar 

  2. Z. I. Borevich and I. R. Shafarevich, Number theory, Academic Press, New York, 1966.

    MATH  Google Scholar 

  3. M. Eichler, Allgemeine Kongruenzklasseneinteilungen der Ideale einfachen Algebren über algebraischen Zahlkörpern und ihre L-Reihen, J. Reine Angew. Math. 179 (1938), 227–251.

    MathSciNet  MATH  Google Scholar 

  4. W. Feit, Characters of finite groups, Math. Lecture Note Series, Benjamin, New York, 1967.

    MATH  Google Scholar 

  5. A. Fröhlich, On the classgroups of integral group rings of finite Abelian groups, Mathematika 16 (1969), 143–152.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____, On the classgroups of integral group rings of finite Abelian groups, II, Mathematika (to appear).

    Google Scholar 

  7. _____, Picard groups (to appear).

    Google Scholar 

  8. A. Fröhlich, I. Reiner, and S. Ullom, Class groups and Picard groups of orders (to appear).

    Google Scholar 

  9. S. Galovich, Nibs and Pics, Ph.D. Thesis, Brown University, Providence, Rhode Island, 1972.

    Google Scholar 

  10. S. Galovich, I. Reiner, and S. Ullom, Class groups for integral representations of metacyclic groups, Mathematika (to appear).

    Google Scholar 

  11. G. Higman, The units of group rings, Proc. London Math. Soc. (2) 46 (1940), 231–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. H. Jacobinski, Genera and decompositions of lattices over orders, Acta Math. 121 (1968), 1–29.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. M. A. Kervaire and M. P. Murthy, On the projective class group of cyclic groups of prime power order (to appear).

    Google Scholar 

  14. J. Milnor, Introduction to algebraic K-theory, Annals of Math. Studies #72, Princeton Univ. Press, Princeton, N.J., 1971.

    MATH  Google Scholar 

  15. I. Reiner, A survey of integral representation theory, Bull. Amer. Math. Soc. 76 (1970), 159–227.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. I. Reiner and S. Ullom, Class groups of integral group rings, Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

  17. _____, A Mayer-Vietoris sequence for class groups, J. of Algebra (to appear).

    Google Scholar 

  18. K. W. Roggenkamp and V. H. Dyson, Lattices over orders. I, II. Lecture Notes No. 115, 142, Springer-Verlag, 1970.

    Google Scholar 

  19. R. G. Swan, Induced representations and projective modules, Ann. of Math. (2) 71 (1960), 552–578.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. R. G. Swan and E. G. Evans, K-theory of finite groups and orders, Lecture Notes No. 149, Springer-Verlag, 1970.

    Google Scholar 

  21. S. Ullom, A note on the classgroup of integral group rings of some cyclic groups, Mathematika 17 (1970), 79–81.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Reiner, I., Ullom, S. (1973). Class groups of orders and a mayer-vietoris sequence. In: Proceedings of the Conference on Orders, Group Rings and Related Topics. Lecture Notes in Mathematics, vol 353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059266

Download citation

  • DOI: https://doi.org/10.1007/BFb0059266

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06518-0

  • Online ISBN: 978-3-540-37818-1

  • eBook Packages: Springer Book Archive