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Relative coherence and preenvelopes

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Abstract

We define coherence relative to an arbitrary torsion theory and characterize it in terms of preenvelopes of modules. In particular, some known results are obtained as corollaries.

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References

  1. Asensio Mayor, J., Martinez Hernandez, J.: Flat envelopes in commutative rings. Israel J. Math. 62, 123–128(1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Azumaya, G.: Finite splitness and finite projectivity. J. Algebra 106, 114–134(1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Azumaya, G.: Some characterizations of regular modules. Publ. Mat. 34, 241–248(1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Camillo, V.: Coherence for polynomial rings. J. Algebra 132, 72–76(1990)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chase, S. U.: Direct products of modules. Trans. Amer. Math. Soc. 97, 457–473 (1960)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Damiano, R. F.: Coflat rings and modules. Pacific J. Math. 81, 349–369 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Enochs, E. E.: Injective and flat covers, envelopes and resolvents. Israel J. Math. 39, 189–209(1981)

    Article  MathSciNet  MATH  Google Scholar 

  9. Enochs, E. E., Jenda, O.: Resolvents and dimensions of modules and rings. Arch. Math. 56, 528–532(1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Faith, C.: Embedding torsionless modules in projectives. Publ. Math. 34, 379–387(1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Garfinkel, G. S.: Universally torsionless and trace modules. Trans. Amer. Math. Soc. 215, 119–144(1976)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Jones, M. F.: Coherence relative to a hereditary torsion theory. Comm. Algebra 10, 719–739(1982)

    Article  MathSciNet  MATH  Google Scholar 

  14. Jones, M. F.: Flatness and f—projectivity of torsion free modules and injective modules. Lecture Notes in Math. 951, 94–116(1982)

    Article  MATH  Google Scholar 

  15. Jones, M. F., Teply, M. L.: Coherent rings of finite weak global dimension. Comm. Algebra 10, 493–503(1982)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jones, M. F., Teply, M. L., Harui, H.: Relative coherence and TTF classes. Comm. Algebra 10, 2019–2029(1982)

    Article  MathSciNet  MATH  Google Scholar 

  17. Martinez Hernandez, J.: Relatively flat envelopes. Comm. Algebra 14, 867–884(1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rotman, J. J.: An Introduction to Homological Algebra. New York San Francisco London: Academic Press 1979

    MATH  Google Scholar 

  19. Stenström, B.: Rings of Quotients. Berlin-Heidelberg-New York: Springer 1975

    Book  MATH  Google Scholar 

  20. Zimmermann-Huisgen, B.: Pure submodules of direct products of free modules. Math. Ann. 224, 233–245(1976)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210008, Nanjing, P.R. China

    Nanqing Ding

  2. Department of Mathematics and Mechanics, Southeast University, 210018, Nanjing, P.R. China

    Jianlong Chen

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  1. Nanqing Ding
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  2. Jianlong Chen
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Ding, N., Chen, J. Relative coherence and preenvelopes. Manuscripta Math 81, 243–262 (1993). https://doi.org/10.1007/BF02567857

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  • DOI: https://doi.org/10.1007/BF02567857

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