Direct sum decompositions of indecomposable injective modules

  • Lee, Sang-Cheol (Department of Mathematics Education, Chonbuk National University, Chonju, Chonbuk 561-756)
  • Published : 1998.02.01

Abstract

Matlis posed the following question in 1958: if N is a direct summand of a direct sum M of indecomposable injectives, then is N itself a direct sum of indecomposable innjectives\ulcorner It will be proved that the Matlis problem has an affirmative answer when M is a multiplication module, and that a weaker condition then that of M being a multiplication module can be given to module M when M is a countable direct sum of indecomposable injectives.

References

  1. Rings and Categories of Moducles F. W. Anderson;K. R. Fuller
  2. Rings and Categories of Moducles(Second Edition) F. W. Anderson;K. R. Fuller
  3. On a Problem of Matlis of Krull-Schnidt's Theorem v.7 Z.-Z. Chen
  4. Algebra II Ring theory C. Faith
  5. J. Algebra v.5 Direct sum representations of injective modules C. Faith;E. Walker
  6. An Introduction to Noncommutative Noetherian Rings K. R. Goodearl;R. B. Warfield, Jr.
  7. Factor categories with applications to direct decomposition of modules M. Harada
  8. J. Indian Math. Soc.(N.S.) v.35 Problem of Krull-Schmidt-Remak-Azumaya-Matlis U. S. Kahlon
  9. Pacific J. Math. v.8 Injective modules over Noetherian rinys E. Matlis
  10. Publ. Math. Debrecen v.6 On algebraically closed modules Z. Papp
  11. Arch. Math. v.50 Some remarks on multiplication modules P. F. Smith
  12. Communications in Algebra v.21 Generalizations fo CS-Modules P. F. Smith;A. Tercan
  13. Injective Modules D. W. Sharpe;P. Vamos
  14. J. London Math. Soc v.43 The dual of the notion of "Finitely gencrated" P. Vamos
  15. Pacific J. Math. v.31 Decompositions of injective modules R. B. Warfield, Jr.
  16. Prco. Japan Acad. v.49 A note on a problem of Matlis K. Yamagata
  17. Communications in Algebra v.24 On Krull-Schmidt and a Problem of Matlis Hua-Ping Yu