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I-radicals and right perfect rings

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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.

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References

  1. O. L. Horbachuk and M. Ya. Komarnitskiy, “I-radicals and their properties,” Ukr. Mat. Zh., 30, No. 2, 212–217 (1978).

    Article  Google Scholar 

  2. O. L. Horbachuk and Yu. P. Maturin, “On S-torsion theories in R-Mod,” Mat. Studii, 15, No. 2, 135–139 (2001).

    MATH  MathSciNet  Google Scholar 

  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).

    Article  MATH  MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  5. O. L. Horbachuk and Yu. P. Maturin, “On I-radicals,” Bul. Acad. Sci. Rep. Moldova, 2(45), 89–94 (2004).

    MathSciNet  Google Scholar 

  6. O. L. Horbachuk, Talk at the 5th International Algebraic Conference in Ukraine, Odessa (2005).

  7. M. Ya. Komarnitskiy, “Duo rings over which all torsions are S-torsions,” Mat. Issled., 48, 65–68 (1978).

    Google Scholar 

  8. S. E. Dickson, “A torsion theory for abelian categories,” Trans. Amer. Math. Soc., 121, 223–235 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  9. M. L. Teply, “Homological dimension and splitting torsion theories,” Pacif. J. Math., 34, 233–205 (1970).

    MathSciNet  Google Scholar 

  10. J. P. Jans, “Some aspects of torsion,” Pacif. J. Math., 15, 1249–1259 (1965).

    MATH  MathSciNet  Google Scholar 

  11. B. Stenström, Rings of Quotients, Springer, New York (1975).

    MATH  Google Scholar 

  12. H. Bass, “Finitistic dimension and a homological generalization of semi-primary rings,” Trans. Amer. Math. Soc., 95, 466–488 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  13. J. S. Golan, “On some torsion theories studied by Komarnickiy,” Houston J. Math., 7, 239–247 (1981).

    MATH  MathSciNet  Google Scholar 

  14. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer, New York (1974).

    MATH  Google Scholar 

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 1005–1008, July, 2007.

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Rump, W. I-radicals and right perfect rings. Ukr Math J 59, 1114–1119 (2007). https://doi.org/10.1007/s11253-007-0072-6

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  • DOI: https://doi.org/10.1007/s11253-007-0072-6

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