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Cancellation modules over regular rings

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Ring Theory

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References

  1. E.P. Armendariz, Modules with artinian prime factors. Proc. Amer. Math. Soc. 78,3(1980) 311–314.

    Article  MathSciNet  MATH  Google Scholar 

  2. E.P. Armendariz, J.W. Fisher and R.L. Snider, On injective and surjective endomorphisms of finitely generated modules, Comm. in Algebra 6(7)(1978) 659–672.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Azumaya, Strongly π-regular rings, J. Fac. Sci. Hokkaido Univ. 13(1954) 34–39.

    MathSciNet  MATH  Google Scholar 

  4. H. Bass, K-theory and stable algebra, Publ. Math. I.H.E.S., no22 Paris (1964).

    Google Scholar 

  5. W.D. Burgess and W. Stephenson, An analogue of the Pierce sheaf for non-commutative rings, Comm. in Algebra 6(9) (1978) 863–886.

    Article  MathSciNet  MATH  Google Scholar 

  6. W.D. Burgess and P. Menal, Strongly π-regular rings and homomorphisms into them (preprint).

    Google Scholar 

  7. P.M. Cohn, The complement of a finitely generated direct summand of an Abelian group, Proc. Amer. Math. Soc. 7(1956) 520–521.

    Article  MathSciNet  MATH  Google Scholar 

  8. W. Dicks and A.H. Schofield, On semihereditary rings (preprint).

    Google Scholar 

  9. F. Dischinger, Stark π-reguläre Ringe. Dissertation (1977) Ludwig-Maximilians-Universität München.

    Google Scholar 

  10. F. Dischinger, Sur les anneaux fortement π-réguliers, C.R. Acad. Sci. Paris 283 A (1976) 571–573.

    MathSciNet  MATH  Google Scholar 

  11. E.G. Evans, Krull-Schmidt and cancellation over local rings, Pac. J. Math. 46 (1973) 115–121.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Faith, Algebra: Rings, modules and categories I, Springer-Verlag Berlin Heidelberg New York, 1973.

    Book  MATH  Google Scholar 

  13. L. Fuchs, On a substitution property for modules, Monatshefte für Math., 75(1971) 198–204.

    Article  MathSciNet  MATH  Google Scholar 

  14. K.R. Goodearl, Power cancellation of groups and modules, Pac. J. Math. 64(1976) 387–411.

    Article  MathSciNet  MATH  Google Scholar 

  15. K. R. Goodearl, Ring Theory, Nonsingular rings and modules, Dekker, New York 1976.

    MATH  Google Scholar 

  16. K. R. Goodearl, von Neumann regular rings (Pitman) London San francisco Melbourne 1979.

    Google Scholar 

  17. K. R. Goodearl and R. B. Warfield, Algebras over zero-dimensional rings, Math. Ann. 223 (1976) 157–168.

    Article  MathSciNet  MATH  Google Scholar 

  18. K. R. Goodearl, Artinian and Noetherian modules over regular rings, Comm. in Algebra 8(5) (1980) 477–504.

    Article  MathSciNet  MATH  Google Scholar 

  19. K. R. Goodearl, Surjective endomorphisms of finitely generated modules, Comm. in Algebra (to appear).

    Google Scholar 

  20. K. R. Goodearl and P. Menal, Stable range 1 for algebras over uncountable fields (title tentative).

    Google Scholar 

  21. K. R. Goodearl and J. Moncasi, Preprint.

    Google Scholar 

  22. M. Henriksen, On a class of regular rings that are elementary divisor rings, Arch. der Math., 24 (1973) 133–141.

    Article  MathSciNet  MATH  Google Scholar 

  23. N. Jacobson, Structure of rings,Amer. Math. Coll. Pub. 37, Providence, RI 1964.

    Google Scholar 

  24. I. Kaplansky, Bass's first stable range condition, mimeographed notes, 1971.

    Google Scholar 

  25. P. Menal, On π-regular rings whose primitive factor rings are artinian, J. Pure and Appl. Algebra 20(1981) 71–78.

    Article  MathSciNet  MATH  Google Scholar 

  26. P. Menal and J. Moncasi, On regular rings with stable range 2, J. Pure and Appl. Algebra 24(1982) 25–40.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Moncasi, Rang estable en anells regulars, Tesi Universitat Autònoma de Barcelona (1984).

    Google Scholar 

  28. B. Stenström, Rings and quotients, Springer Verlag, Berlin Heidelberg 1975.

    Book  MATH  Google Scholar 

  29. W. Vasconcelos, On local and stable cancellation, Ann. Acad. Brasil. Ci. 37(1965) 389–393.

    MathSciNet  MATH  Google Scholar 

  30. L. N. Vaserstein, Bass's first stable range condition, J. Pure Appl. Algebra 34 (1984) 319–330.

    Article  MathSciNet  MATH  Google Scholar 

  31. E.A. Walker, Cancellation in direct sums of groups. Proc. Amer. Math. Soc. 7(1956) 898–902.

    Article  MathSciNet  MATH  Google Scholar 

  32. R.B. Warfield, A Krull-Schmidt Theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969) 460–465.

    Article  MathSciNet  MATH  Google Scholar 

  33. R.B. Warfield, Cancellation of modules and groups and stable range of endomorphism rings, Pac. J. Math. 91(1980) 457–485.

    Article  MathSciNet  MATH  Google Scholar 

  34. R. Wiegand, Abelian groups and modules, Proc. of the Udine Conference (CISM Courses and Lectures No 287) Springer Verlag 1984, 441–466.

    Google Scholar 

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Jose Luis Bueso Pascual Jara Blas Torrecillas

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© 1988 Springer-Verlag

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Menal, P. (1988). Cancellation modules over regular rings. In: Bueso, J.L., Jara, P., Torrecillas, B. (eds) Ring Theory. Lecture Notes in Mathematics, vol 1328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100925

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  • DOI: https://doi.org/10.1007/BFb0100925

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  • Print ISBN: 978-3-540-19474-3

  • Online ISBN: 978-3-540-39278-1

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