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Journal of Mathematical Sciences

, Volume 237, Issue 2, pp 284–286 | Cite as

Goldie Rings Graded by a Group with Periodic Quotient Group Modulo the Center

  • A. L. KanunnikovEmail author
Article
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Abstract

In this paper, we study gr-prime and gr-semiprime Goldie rings graded by a group with periodic quotient group modulo the center. We enhance the theorem of Goodearl and Stafford (2000) about gr-prime rings graded by Abelian groups; we extend the Abelian group class to the class of groups with periodic quotient group modulo the center. We also decompose the orthogonal graded completion Ogr(R) of a gr-semiprime Goldie ring R (graded by a group satisfying the same condition) into a direct sum of gr-prime Goldie rings R1, . . . , Rn and prove that the maximal graded quotient ring Qgr(R) equals the direct sum of classical graded quotients rings of R1, . . . , Rn.

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References

  1. 1.
    I. N. Balaba, A. L. Kanunnikov, and A. V. Mikhalev, “Quotient rings of graded associative rings. I,” J. Math. Sci., 186, No. 4, 531–577 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    K. Goodearl and T. Stafford, “The graded version of Goldie’s theorem,” Contemp. Math., 259, 237–240 (2000).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    A. L. Kanunnikov, “Graded versions of Goldie’s theorem,” Moscow Univ. Math. Bull., 66, No. 3, 119–122 (2011).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    A. L. Kanunnikov, “Graded versions of Goldie’s theorem. II,” Moscow Univ. Math. Bull., 68, No. 3, 162–165 (2013).Google Scholar
  5. 5.
    A. L. Kanunnikov, “Orthogonal graded completion of graded semiprime rings,” J. Math. Sci., 197, No. 4, 525–547 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    C. Năstăsescu, E. Nauwelaerts, and F. van Oystaeyen, “Arithmetically graded rings revisited,” Commun. Algebra, 14, No. 10, 1191–2017 (1986).MathSciNetzbMATHGoogle Scholar
  7. 7.
    C. Năstăsescu and F. van Oystaeyen, Graded and Filtered Rings and Modules, Lect. Notes Math., Vol. 758, Springer, Berlin (1979).CrossRefGoogle Scholar
  8. 8.
    C. Năstăsescu and F. van Oystaeyen, Graded Ring Theory, North-Holland, Amsterdam (2004).CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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