Acta Mathematica Sinica

, Volume 18, Issue 2, pp 339–346 | Cite as

Dubrovin Valuation Skew Group Rings

  • Zhong YiEmail author


Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given. Among them all the prime ideals of a Dubrovin valuation skew group ring are characterised.


Dubrovin valuation ring Skew group ring Inertial subgroup Decomposition subgroup 

MR (2000) Subject Classification

16S35 13A18 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Montgomery S., Fixed Rings of Finite Automorphism Groups of Associate Rings, Lecture Notes in Math., Berlin: Springer, 1980, 818 Google Scholar
  2. 2.
    Passman D. S., Infinite Crossed Products, San Diego: Academic Press, 1989Google Scholar
  3. 3.
    Rotman J. J., An Introduction to Homological Algebra, New York: Academic Press, 1979Google Scholar
  4. 4.
    Dubrovin N. I., Noncommutative valuation rings, Trans. Moscow Math. Soc., 1984, 1:273–287Google Scholar
  5. 5.
    Dubrovin N. I., Noncommutative valuation rings in simple finite-dimensional algebras over a field, Math. USSR. Sbornik, 1985, 51(2):493–505zbMATHCrossRefGoogle Scholar
  6. 6.
    Wadsworth A., Dubrovin valuation rings and Henselization, Math. Ann., 1989, 283:301–328zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Aljadeff E., Rosset S., Global dimension of crossed products, J. Pure Appl. Algebra, 1986, 40:104–113CrossRefMathSciNetGoogle Scholar
  8. 8.
    Marubayashi H., Yi Z., Dubrovin valuation properties of skew group rings and crossed products, Comm. Algebra, 1998, 26(1):293–307zbMATHMathSciNetGoogle Scholar
  9. 9.
    Martin R., Some skew group rings which are maximal orders, Preprint, Department of Math., University of Glasgow, 1992Google Scholar
  10. 10.
    Yi Z., Homological dimension of skew group rings and crossed products, J. Algebra, 1994, 164(1):101–123zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Martin R., Skew group rings and maximal orders, Glasgow Math. J., 1995, 37:249–263zbMATHMathSciNetGoogle Scholar
  12. 12.
    Ramras M., Orders with finite global dimension, Pacific J. Math., 1974, 50(2):583–587zbMATHMathSciNetGoogle Scholar
  13. 13.
    Lorenz M., Passman D. S., Prime ideals in group algebra of polycyclic-by-finite groups, Proc. Lodon Math. Soc., 1981, 43:520–543zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Department of MathematicsGuangxi Normal UniversityGuilinP.R. China

Personalised recommendations