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Graded Rings with Finiteness Conditions

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Abstract

This paper is devoted to quotient rings of graded rings with finiteness conditions for ideals. The analogs of Goldie, Shock, and Small theorems are proved. We find criteria for a graded ring R to admit a gr-semisimple and gr-Artinian (the Goldie theorem) and gr-Artinian (the Small theorem) classical graded quotient ring.

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References

  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).

    Article  MathSciNet  MATH  Google Scholar 

  2. D. S. Bazhenov, “Graded prime Goldie rings,” Mosc. Univ. Math. Bull., 72, 70–72 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  3. A. L. Kanunnikov, “Graded versions of Goldie’s theorem,” Mosc. Univ. Math. Bull., 66, No. 3, 119–122 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. L. Kanunnikov, “Criteria for the validity of Goldie’s theorems for graded rings,” Algebra Logic, 57, No. 5, 353–359 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. L. Kanunnikov, “Graded quotient rings,” J. Math. Sci., 233, No. 1, 50–94 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. N. Maltcev and E. V. Zhuravlev, Lectures on Associative Ring Theory [in Russian], Barnaul (2014).

  7. C. Năstăsescu and F. van Oystaeyen, Graded Ring Theory, North-Holland, Amsterdam (2004).

    Book  MATH  Google Scholar 

  8. L. Small, “Orders in Artinian rings,” J. Algebra, 4, 13–41 (1966).

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Small, “Orders in Artinian rings. Corrections and addendum,” J. Algebra, 4, 505–507 (1996).

    Article  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    D. S. Bazhenov & A. L. Kanunnikov

Authors
  1. D. S. Bazhenov
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  2. A. L. Kanunnikov
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Correspondence to D. S. Bazhenov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 3, pp. 23–35, 2020.

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Bazhenov, D.S., Kanunnikov, A.L. Graded Rings with Finiteness Conditions. J Math Sci 269, 282–289 (2023). https://doi.org/10.1007/s10958-023-06280-w

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  • DOI: https://doi.org/10.1007/s10958-023-06280-w

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