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Original Articles

Tensor and Torsion Products of Relative Injective Modules with Respect to a Semidualizing Module

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Pages 2632-2642 | Received 22 Jul 2013, Published online: 17 Apr 2015

REFERENCES

  • Araya , T. , Takahashi , R. ( 2009 ). A generalization of a theorem of Foxby . Arch. Math. (Basel) 93 ( 2 ): 123 – 127 .
  • Avramov , L. L. , Foxby , H. B. ( 1997 ). Ring homomorphisms and finite Gorenstein dimension. Proc. London Math. Soc. (3) 75(2):241–270 .
  • Bruns , W. , Herzog , J. ( 1993 ). Cohen–Macaulay Rings . Cambridge : Cambridge University Press .
  • Christensen , L. W. 2000 . Gorenstien Dimensions. Lecture Notes in Mathematics. Vol. 1747, Springer .
  • Christensen , L. W. ( 2001 ). Semi-dualizing complexes and their Auslander categories . Trans. Amer. Math. Soc. 353 ( 5 ): 1839 – 1883 .
  • Enochs , E. E. , Jenda , O. M. G. ( 1991 ). Tensor and torsion products of injective modules . J. Pure Appl. Algebra 76 ( 2 ): 143 – 149 .
  • Enochs , E. E. , Jenda , O. M. G. ( 2000 ). Relative homological algebra. de Gruyter Expositions in Mathematics. Vol. 30. Berlin: Walter de Gruyter & Co .
  • Foxby , H. B. ( 1972 ). Gorenstein modules and related modules . Math. Scand. 31 : 267 – 284 .
  • Golod , E. S. ( 1984 ). G-dimension and generalized perfect ideals . Trudy Mat. Inst. Steklov. 165 : 62 – 66 .
  • Holm , H. , Jøtrgensen , P. ( 2006 ). Semidualizing modules and related Gorenstein homological dimension . J. Pure Appl. Algebra 205 ( 2 ): 423 – 445 .
  • Holm , H. , White , D. (2007). Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47(4):781–808.
  • Ishikawa , T. ( 1965 ). On injective modules and flat modules . J. Math. Soc. Japan 17 : 291 – 296 .
  • Nasseh , S. , Sather-Wagstaff , S. A local ring has only finitely many semidualizing complexes up to shift-isomorphism. arXive: 1201.0037 .
  • Sather-Wagstaff , S. ( 2007 ). Semidualizing modules and the divisors class group . Illinois J. Math. 51 ( 1 ): 255 – 285 .
  • Sather-Wagstaff , S. ( 2008 ). Complete intersection dimensions and Foxby classes . J. Pure Appl. Algebra 212 ( 12 ): 2594 – 2611 .
  • Sather-Wagstaff , S. ( 2009 ). Bass numbers and semidualizing complexes. Commutative Algebra and Its Applications. Berlin: Walter de Gruyter, pp. 349–381 .
  • Sather-Wagstaff , S. Semidualizing modules. URL:http://www.ndsu.edu/pubweb/asciitildessatherw/
  • Sather-Wagstaff , S. , Sharif , T. , White , D. ( 2011 ). AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules . Algebr. Represent. Theory 14 ( 3 ): 403 – 428 .
  • Sather-Wagstaff , S. , Yassemi , S. ( 2009 ). Modules of finite homological dimension with respect to a semidualizing module . Arch. Math. (Basel) 93 ( 2 ): 111 – 121 .
  • Takahashi , R. , White , D. ( 2010 ). Homological aspects of semidualizing modules . Math. Scand. 106 ( 1 ): 5 – 22 .
  • Tang , X. ( 2012 ). New characterizations of dualizing modules . Comm. Algebra 40 ( 3 ): 845 – 861 .
  • Vascocelos , W. V. ( 1974 ). Divisor theory in module categories. North-Holland Math. Stud. Vol. 14. Amsterdam: North-Holland Publishing Co .
  • Communicated by T. Albu.

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