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Original Articles

On Valuation Rings

&
Pages 176-183 | Received 24 Jun 2009, Published online: 20 Jan 2011

REFERENCES

  • Bakkari , C. , Kabbaj , S. , Mahdou , N. ( 2010 ). Trivial extention defined by Prüfer conditions . J. Pure. Appl. Algebra 214 : 53 – 60 .
  • Bazzoni , S. , Glaz , S. ( 2007 ). Gaussian properties of total rings of quotients . J. Algebra 310 : 180 – 193 .
  • Costa , D. ( 1994 ). Parameterizing families of non-Noetherian rings . Comm. Algebra 22 : 3997 – 4011 .
  • Costa , D. , Kabbaj , S. ( 1996 ). Classes of D + M rings defined by homological conditions . Comm. Algebra 24 : 891 – 906 .
  • Couchot , F. ( 2003 ). The λ-dimension of commutative arithmetic rings . Comm. Algebra 31 : 3143 – 3158 .
  • Couchot , F. ( 2006 ). Localization of injective modules over valuation rings . Proc. Amer. Math. Soc. 134 ( 4 ): 1013 – 1017 .
  • Damiano , R. , Shapiro , J. ( 1984 ). Commutative torsion stable rings . J. Pure Appl. Algebra 32 : 21 – 32 .
  • Fuchs , L. , Salce , L. ( 1985 ). Modules overs valuation domains . Pure and Applied Mathematics 97 .
  • Glaz , S. ( 1989 ). Commutative Coherent Rings . Lecture Notes in Mathematics, 1371 . Berlin : Springer-Verlag .
  • Glaz , S. ( 2000 ). Finite conductor rings . Proc. Amer. Math. Soc. 129 : 2833 – 2843 .
  • Glaz , S. (2005). The weak global dimension of Gaussian rings. Proc. Amer. Math. Soc. 133:2507–2513.
  • Huckaba , J. A. ( 1988 ). Commutative Rings with Zero Divisors . New York–Basel : Marcel Dekker .
  • Jensen , C. U. ( 1966 ). Arithmetical rings . Acta Math. Hungr. 17 : 115 – 123 .
  • Kabbaj , S. , Mahdou , N. ( 2003 ). Trivial Extensions of Local Rings and a Conjecture of Costa . Lecture Notes in Pure and Appl. Math. , Vol. 231 . New York : Marcel Dekker , pp. 301 – 312 .
  • Kabbaj , S. , Mahdou , N. ( 2004 ). Trivial extensions defined by coherent-like conditions . Comm. Algebra 32 : 3937 – 3953 .
  • Ali Majid , M. ( 2007 ). Idealization and Theorems of D. D . Anderson II, Comm. Algebra 35 : 2767 – 2792 .
  • Mahdou , N. ( 2001 ). On Costa's conjecture . Comm. Algebra 29 : 2775 – 2785 .
  • Mahdou , N. ( 2005 ). On 2-Von Neumann regular rings . Comm. Algebra 33 : 3489 – 3496 .
  • Osofsky , B , ( 1969 ). Global dimension of commutative rings with linearly ordered ideals . J. London Math. Soc. 44 : 183 – 185 .
  • Palmér , I. , Roos , J.-E. ( 1973 ). Explicit formulae for the global homological dimensions of trivial extensions of rings . J. Algebra 27 : 380 – 413 .
  • Rotman , J. J. ( 1979 ). An Introduction to Homological Algebra . New York : Academic Press .
  • Warfield , R. B. ( 1970 ). Decomposibility of finitely presented modules . Proc. Amer. Math Soc. 25 : 167 – 172 .
  • Zhou , D. ( 2004 ). On n-coherent rings and (n, d)-rings . Comm. Algebra 32 : 2425 – 2441 .
  • Communicated by I. Swanson.

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