When Summands of Completely Decomposable Modules Are Completely Decomposable

REFERENCES

• Arnold , D. M. ( 1982 ). Finite Rank Torsion-Free Abelian Groups and Rings . LNM 931 . Springer-Verlag .
   Google Scholar
• Fuchs , L. ( 1972 ). Infinite Abelian Groups . Vol. 2 . Academic Press .
   Google Scholar
• Fuchs , L. , Salce , L. ( 1985 ). Modules Over Valuation Domains . Lecture Notes in Pure and Applied Mathematics . Vol. 97 . Marcel Dekker, Inc.
   Google Scholar
• Fuchs , L. , Salce , L. ( 2001 ). Modules Over Non-Noetherian Domains . Mathematical Surveys and Monographs . Vol. 84 . AMS .
   Google Scholar
• Goeters , P. ( 1995 ). Warfield duality and module extensions over a Noetherian domain . Abelian Groups and Modules . (Padova, 1994), Math. Appl., 343 . Dordrecht : Kluwer Acad. Publ. , pp. 239 – 248 .
   Google Scholar
• Goeters , P. ( 1999 ). Butler modules over 1-dimensional Noetherian domains . Abelian Groups and Modules . (Dublin, 1998), Trends Math. Basel : Birkhäuser , pp. 149 – 165 .
   Google Scholar
• Goeters , P. , Olberding , B. ( 2001 ). Uniqueness of decompositions into ideals for Noetherian domains . J. Pure and Applied Alg. 165 ( 2 ):169–182.
   Web of Science ®Google Scholar
• Goeters , P. , Olberding , B. ( 2002a ). On locally isomorphic torsion-free modules . Commutative Rings . Hauppauge , NY : Nova Sci. Publ. , pp. 83 – 94 .
   Google Scholar
• Goeters , P. , Olberding , B. ( 2002b ). The Krull-Schmidt property for ideals and modules over integral domains . In: Proceedings of the Second Honolulu Conference on Abelian Groups and Modules. (Honolulu, HI, 2001) . Rocky Mountain J. Math. 32 ( 4 ): 1409 – 1429 .
   Web of Science ®Google Scholar
• Levy , L. , Odenthal , C. ( 1996 ). Krull-Schmidt theorems in dimension 1 . Trans. AMS 348 ( 9 ): 3391 – 3455 .
   Web of Science ®Google Scholar
• Matlis , E. ( 1964 ). Cotorsion Modules . Memoirs of the AMS . Vol. 49 .
   Google Scholar
• Matlis , E. ( 1972 ). Torsion-Free Modules . Chicago : University of Chicago Press .
   Google Scholar
• Matlis , E. ( 1973 ). 1-Dimensional Cohen-Macaulay Rings . LNM 327 . Springer-Verlag .
   Google Scholar
• Matsumura , H. ( 1980 ). Commutative Ring Theory . Cambridge : Cambridge University Press .
   Google Scholar
• Olberding , B. ( 1999 ). Prüfer domains and pure submodules of direct sums of ideals , Mathematika 46 ( 2 ): 425 – 432 .
   Google Scholar
• Rotman , J. J. ( 1979 ). An Introduction to Homological Algebra . Academic Press .
   Google Scholar
• Rush , D. E. ( 1991 ). Rings with two-generated ideals . J. Pure and Applied Alg. 73 : 257 – 275 .
   Web of Science ®Google Scholar
• Communicated by K. M. Rangaswamy.
   Google Scholar