Skip to main content
Log in

Projectivity of finitely generated flat modules over semilocal rings

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. I. I. Sakhaev, “Rings over which every finitely generated flat module is projective,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 65–73 (1969).

    Google Scholar 

  2. W. V. Vasconcelos, “On finitely generated flat modules,” Trans. Am. Math. Soc.,138, 505–512 (1969).

    Google Scholar 

  3. S. Jondrup, “Flat and projective modules,” Math. Scand.,43, No. 2, 336–342 (1978).

    Google Scholar 

  4. N. Jacobson, Structure of Rings, Am. Math. Soc., Providence, R.I. (1956).

    Google Scholar 

  5. I. I. Sakhaev, “Projectivity of finitely generated flat modules,” Sib. Mat. Zh.,6, No. 3, 565–573 (1965).

    Google Scholar 

  6. C. Faith, Algebra: Rings, Modules, and Categories, Springer-Verlag (1973).

  7. H. Cartan and S. Eilenberg, Homological Algebra, Princeton Univ. Press (1956).

  8. D. Lazard, “Autour de la platitude, La thèse de doctorat en sciences,” Bull. Soc. Math. France,97, 81–128 (1969).

    Google Scholar 

  9. I. I. Sakhaev, “Finite generation of projective modules,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 69–79 (1977).

    Google Scholar 

  10. J. Beck, “Projective and free modules,” Math. Z.,129, No. 3, 231–234 (1972).

    Google Scholar 

  11. H. Bass, “Finite dimension and a homological generalization of semiprimary rings,” Trans. Am. Math. Soc.,95, No. 3, 466–488 (1960).

    Google Scholar 

  12. S. Chase, “Direct products of modules,” Trans. Am. Math. Soc.,97, No. 3, 457–473 (1960).

    Google Scholar 

  13. J. Lambek, Lectures in Rings and Modules, Chelsea Publ. (1976).

  14. N. Bourbaki, Algebra: Modules, Rings, Forms [Russian translation], Nauka, Moscow (1966).

    Google Scholar 

  15. J. Milnor, Introduction to Algebraic K-Theory, Princeton Univ. Press (1972).

  16. L. S. Pontryagin, Continuous Groups [in Russian], Nauka, Moscow (1954).

    Google Scholar 

  17. N. Bourbaki, Commutative Algebra, Addison-Wesley (1972).

  18. I. I. Sakhaev and G. V. Chirkov, “Projectivity of finitely generated flat modules,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 1, 85–93 (1972).

    Google Scholar 

  19. K. H. Mount, “Some remarks on Fitting invariants,” Pac. J. Math.,13, 1353–1357 (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 37, No. 2, pp. 152–162, February, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sakhaev, I.I. Projectivity of finitely generated flat modules over semilocal rings. Mathematical Notes of the Academy of Sciences of the USSR 37, 85–90 (1985). https://doi.org/10.1007/BF01156749

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01156749

Keywords

Navigation