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Balance for relative homology with respect to semidualizing modules

Jianlong Chen|Zhenxing Di|Xiaoxiang Zhang
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회보 (Bulletin of the KMS)|제52권 제1호|pp. 137-147

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참고문헌

키워드

balancesemidualizing moduleGorenstein dimensionrelative homology
주제분류수학

초록

We derive in the paper the tensor product functor $-\otimes_R-$ by using proper $\mathcal {G}\mathcal {P}_C$-resolutions, where $C$ is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of $\mathcal {G}_C$-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module $D$.

Abstract

We derive in the paper the tensor product functor $-\otimes_R-$ by using proper $\mathcal {G}\mathcal {P}_C$-resolutions, where $C$ is a semidualizing module. After giving several cases in which different relative homologies agree, we use the Pontryagin duals of $\mathcal {G}_C$-projective modules to establish a balance result for such relative homology over a Cohen-Macaulay ring with a dualizing module $D$.

참고문헌 (22)

  1. L. W. Christensen, "Semi-dualizing complexes and their Auslander categories", Trans. Amer. Math. Soc, 353(5), pp.1839~1883 (2001)
  2. L. W. Christensen, "On Gorenstein projective, injective and flat dimensions − A functorial description with applications", J. Algebra, 302(1), pp.231~279 (2006)
  3. Zhenxing Di, "Transfer properties of Gorenstein homological dimension with respect to a semidualizing module", 대한수학회지, 49(6), pp.1197~1214 (2012), 대한수학회
  4. I. Emmanouil, "On the finiteness of Gorenstein homological dimensions", J. Algebra, 372, pp.376~396 (2012)
  5. E. E. Enochs, "Foxby equivalence and cotorsion theories relative to semi-dualizing modules", Math. Scand, 95(1), pp.33~43 (2004)
  6. H.-B. Foxby, "Gorenstein modules and related modules", Math. Scand, 31, pp.267~284 (1972)
  7. H.-B. Foxby, "Gorenstein dimensions over Cohen-Macaulay rings", Proceedings of the international conference on commutative algebra, pp.59~63 (1994), Universit¨at Osnabr¨uck
  8. E. S. Golod, "G-dimension and generalized perfect ideals", Trudy. Mat. Inst. Steklov, 165, pp.62~66 (1984)
  9. H. Holm, "Gorenstein derived functors", Proc. Amer. Math. Soc, 132(7), pp.1913~1923 (2004)
  10. H. Holm, "Semi-dualizing modules and related Gorenstein homological dimensions", J. Pure Appl. Algebra, 205(2), pp.423~445 (2006)
  11. H. Holm, "Foxby equivalence over associative rings", J. Math. Kyoto Univ, 47(4), pp.781~808 (2007)
  12. D. A. Jorgensen, "Presentations of rings with non-trivial semidualizing modules", Collect. Math, 63(2), pp.165~180 (2012)
  13. L. Liang, "Balance for Tate cohomology with respect to semidualzing mod-ules", J. Aust. Math. Soc, 95(2), pp.223~240 (2013)
  14. M. Salimi, "Relative Tor functors with respect to semidualizing modules", Algebr. Represent. Theory, 17(1), pp.103~120 (2014)
  15. S. Sather-Wagstaff, "Gorenstein cohomology in abelian cate-gories", J. Math. Kyoto Univ, 48(3), pp.571~596 (2008)
  16. S. Sather-Wagstaff, "Comparison of relative cohomology theories with respect to semidualizing mod-ules", Math. Z, 264(3), pp.571~600 (2010)
  17. S. Sather-Wagstaff, "Tate cohomology with respect to semidualizing modules", J. Algebra, 324(9), pp.2336~2368 (2010)
  18. R. Takahashi, "Homological aspects of semidualizing modules", Math. Scand, 106(1), pp.5~22 (2010)
  19. W. V. Vasconcelos, "Divisor Theory in Module Categories" (1974), North-Holland Publishing Co
  20. D. White, "Gorenstein projective dimension with respect to a semidualizing module", J. Commut. Algebra, 2(1), pp.111~137 (2010)
  21. D. D. Zhang, "Semidualizing modules and related modules", J. Algebra Appl, 10(6), pp.1261~1282 (2011)
  22. Z. Zhang, "Totally reflexive modules with respect to a semid-ualizing bimodule", Czechoslovak Math. J, 63(2), pp.385~402 (2013)

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