Skip to main content
Log in

Separativity of modules with finite exchange property

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

We introduce the notion of separativity of modules and show that many classes of modules possess the separativity. The present work generalizes many known results.

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.

Similar content being viewed by others

References

  1. Stock, J., On rings whose projective modules have the exchange property, J. Algebra, 1986, 103: 437.

    Article  MATH  MathSciNet  Google Scholar 

  2. Warfield, Jr. R.B., Exchange ring and decompositions of modules, Math. Ann., 1972, 199: 31.

    Article  MATH  MathSciNet  Google Scholar 

  3. Yu, H. P., On modules for which the finite exchange property implies the countable exchange property, Comm. Algebra, 1994, 22: 3887.

    Article  MATH  MathSciNet  Google Scholar 

  4. Pardo, E., Comparability, separativity, and exchange rings, Comm. Algrbra, 1996, 24: 2915

    Article  MATH  MathSciNet  Google Scholar 

  5. Ara, P., Goodearl, K. R., O’ Meara, K.C. et a1., Separative cancellation for projective modules over exchange rings, Israel J. Math., 1998, 105: 105.

    Article  MATH  MathSciNet  Google Scholar 

  6. Ara, P., O’ Meara, K. C., Tyukavkin, D. V., Cancellation of projective modules over regular rings with comparability, J. Purr Appl. Algebra, 1996, 107: 19.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen Huanyin, Comparability of modules over regular rings, Comm. Algebra, 1997, 25: 3531.

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen Huanyin, Exchange rings, related romparability and power-substitution, Comm. Algebra, 1998, 26: 3383.

    Article  MATH  MathSciNet  Google Scholar 

  9. Goodearl, K. R., Direct sum properties of quasi-injective modules, Bull. Amer. Math. Soc., 1976, 82: 108.

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. Zimmermann-Huisgen. B., Zimmermann, W., Algebraically compact rings and modules, Math. Z., 1978, 161: 81

    Article  MathSciNet  Google Scholar 

  12. Warfield, Jr. R. B., Cancellation of modules and groups and stable range of endomorphism rings, Pacific J. Math., 1980, 91: 457.

    MATH  MathSciNet  Google Scholar 

  13. Ehrlich, G., Units and one-sided units in regular rings, Trans. Amer. Math. Soc., 1976, 216: 81.

    Article  MATH  MathSciNet  Google Scholar 

  14. Guralnick, R., Lanski, C., Pesudosimilarity and cancellation of modules, Linear Algebra Appl., 1982,47: 111.

    Article  MATH  MathSciNet  Google Scholar 

  15. Goodearl, K. R., Von Neumann Regular Rings, London-San Francisco-Melbourne: Pitman, 1979.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Huanyin Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, H., Li, F. Separativity of modules with finite exchange property. Sci. China Ser. A-Math. 43, 795–802 (2000). https://doi.org/10.1007/BF02884178

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02884178

Keywords

Navigation