Advertisement

Ukrainian Mathematical Journal

, Volume 59, Issue 7, pp 1114–1119 | Cite as

I-radicals and right perfect rings

Article
  • 22 Downloads

Abstract

We determine the rings for which every hereditary torsion theory is an S-torsion theory in the sense of Komarnitskiy. We show that such rings admit a primary decomposition. Komarnitskiy obtained this result in the special case of left duo rings.

Keywords

Left Ideal Full Subcategory Primary Decomposition Torsion Theory Torsion Class 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. L. Horbachuk and M. Ya. Komarnitskiy, “I-radicals and their properties,” Ukr. Mat. Zh., 30, No. 2, 212–217 (1978).CrossRefGoogle Scholar
  2. 2.
    O. L. Horbachuk and Yu. P. Maturin, “On S-torsion theories in R-Mod,” Mat. Studii, 15, No. 2, 135–139 (2001).zbMATHMathSciNetGoogle Scholar
  3. 3.
    O. L. Horbachuk and Yu. P. Maturin, “I-radicals, their lattices and some classes of rings,” Ukr. Mat. Zh., 54, No. 7, 1016–1019 (2002).zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    O. L. Horbachuk and Yu. P. Maturin, “Rings and properties of lattices of I-radicals,” Bul. Acad. Sci. Rep. Moldova, 38, No. 1, 44–52 (2002).MathSciNetGoogle Scholar
  5. 5.
    O. L. Horbachuk and Yu. P. Maturin, “On I-radicals,” Bul. Acad. Sci. Rep. Moldova, 2(45), 89–94 (2004).MathSciNetGoogle Scholar
  6. 6.
    O. L. Horbachuk, Talk at the 5th International Algebraic Conference in Ukraine, Odessa (2005).Google Scholar
  7. 7.
    M. Ya. Komarnitskiy, “Duo rings over which all torsions are S-torsions,” Mat. Issled., 48, 65–68 (1978).Google Scholar
  8. 8.
    S. E. Dickson, “A torsion theory for abelian categories,” Trans. Amer. Math. Soc., 121, 223–235 (1966).zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    M. L. Teply, “Homological dimension and splitting torsion theories,” Pacif. J. Math., 34, 233–205 (1970).MathSciNetGoogle Scholar
  10. 10.
    J. P. Jans, “Some aspects of torsion,” Pacif. J. Math., 15, 1249–1259 (1965).zbMATHMathSciNetGoogle Scholar
  11. 11.
    B. Stenström, Rings of Quotients, Springer, New York (1975).zbMATHGoogle Scholar
  12. 12.
    H. Bass, “Finitistic dimension and a homological generalization of semi-primary rings,” Trans. Amer. Math. Soc., 95, 466–488 (1960).zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    J. S. Golan, “On some torsion theories studied by Komarnickiy,” Houston J. Math., 7, 239–247 (1981).zbMATHMathSciNetGoogle Scholar
  14. 14.
    F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer, New York (1974).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • W. Rump
    • 1
  1. 1.Institut für Algebra und ZahlentheorieUniversität StuttgartStuttgartGermany

Personalised recommendations