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The flat dimensions of injective modules

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Abstract

Let R be a ring. Define r. IFD(R) as r.IFD(R)=sup{fdE/E is an injective right R—module}. The purpose of this paper is to investigate this “global” dimension.

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References

  1. Anderson, F. W., Fuller, K. R.: Rings and Categories of Modules. New York-Heidelberg-Berlin: Springer 1973

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Bass, H.: Injective dimension in Noetherian rings. Trans. Amer. Math. Soc. 102, 18–29 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cheatham, T. J., Stone, D. R. Flat and projective character modules. Proc. Amer. Math. Soc. 81, 175–177 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cohn, P. M.: On the free product of associative rings. Math. Z. 71, 380–398 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  6. Colby, R. R.: Rings which have flat injective modules. J. Algebra 35, 239–252 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cozzens, J. H.: Homological properties of the ring of differential polynomials. Bull. Amer. Math. Soc. 79, 75–79 (1970)

    Article  MathSciNet  Google Scholar 

  8. Ding, N. Q. f. f. p. Dimension. Acta Methematica Sinica 1, 40–47 (1991)

    Google Scholar 

  9. Enochs, E. E., Jenda, O.: Balanced functors applied to modules. J. Algebra 92, 303–310 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  10. Faith, C.: Algebra I: Rings, Modules and Categories. Berlin-Heidelber-New York: Springer 1981

    MATH  Google Scholar 

  11. Fieldhouse, D. J.: Character modules. Comment. Math. Helv. 46, 274–276 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fieldhouse, D. J.: Character modules, dimension and purity. Glasgow Math. J. 13, 144–146 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  13. Iwanaga, Y.: On ring with finite self—injective dimensionI. Tsukuba J. Math. 4, 107–113 (1980)

    MATH  MathSciNet  Google Scholar 

  14. Jain, S.: Flat and FP—injectivity. Proc. Amer. Math. Soc. 41, 437–442 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jensen, C.U.: On the vanishing of\(\underleftarrow {\lim }^{(i)} \). J. Algebra 15, 151–166 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  16. Rainwater, J.: Global dimension of fully bounded Noetherian rings. Comm. Algebra 15, 2143–2156 (1987)

    MATH  MathSciNet  Google Scholar 

  17. Rotman, J. J.: An Introduction to Homological Algebra. New York: Academic Press 1979

    MATH  Google Scholar 

  18. Stenström, B.: Coherent rings and FP—injective modules. J. London Math. Soc. 2, 323–329 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zaks, A.: Injective dimension of semi-primary rings. J. Algebra 13, 73–86 (1969)

    Article  MATH  MathSciNet  Google Scholar 

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Ding, N., Chen, J. The flat dimensions of injective modules. Manuscripta Math 78, 165–177 (1993). https://doi.org/10.1007/BF02599307

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  • DOI: https://doi.org/10.1007/BF02599307

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