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Communications in Algebra Volume 47, 2019 - Issue 12
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Original Articles

Cohomological dimension and relative Cohen-Maculayness

Kamran Divaani-AazarDepartment of Mathematics, Alzahra University, Tehran, Iran; ;Iran-and-School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran; Correspondence[email protected]
,
Akram Ghanbari DoustFaculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran;
,
Massoud TousiDepartment of Mathematics, Shahid Beheshti University, G.C, Tehran, Iran; ;Iran-and-School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran;
&
Hossein ZakeriFaculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
Pages 5417-5427 | Received 30 Dec 2018, Accepted 04 May 2019, Published online: 04 Jun 2019

References

  • Andre, Y. (2018). La conjecture du facteur direct. Publ. Math. Inst. Hautes Études Sci. 127(1):71–93.
  • Barile, M. (2009). A generalization of a lemma by Schmitt and Vogel. Tokyo J. Math. 32(2):435–440. DOI: 10.3836/tjm/1264170241.
  • Barile, M. (2008). On the arithmetical rank of the edge ideals of forests. Commun. Algebra. 36(12):4678–4703. DOI: 10.1080/00927870802161220.
  • Brodmann, M., Sharp, R. Y. (2013). Local cohomology: An algebraic introduction with geometric applications. In Cambridge Studies in Advanced Mathematics, 2nd ed., vol. 136. Cambridge: Cambridge University Press.
  • Celikbas, O., Holm, H. (2017). Equivalences from tilting theory and commutative algebra from the adjoint functor point of view. New York J. Math. 23:1697–1721.
  • Divaani-Aazar, K., Naghipour, R., Tousi, M. (2002). Cohomological dimension of certain algebraic varieties. Proc. Amer. Math. Soc. 130(12):3537–3544. DOI: 10.1090/S0002-9939-02-06500-0.
  • Dutta, S., Roberts, P. (1996). A characterization of systems of parameters. Proc. Amer. Math. Soc. 124(3):671–675. DOI: 10.1090/S0002-9939-96-02955-3.
  • Hellus, M. (2007). Matlis duals of top local cohomology modules and the arithmetic rank of an ideal. Commun. Algebra. 35(4):1421–1432. DOI: 10.1080/00927870601142348.
  • Hellus, M. (2005). On the associated primes of matlis duals of top local cohomology modules. Commun. Algebra. 33(11):3997–4009. DOI: 10.1080/00927870500261314.
  • Hellus, M., Schenzel, P. (2008). On cohomologically complete intersections. J. Algebra. 320(10):3733–3748. DOI: 10.1016/j.jalgebra.2008.09.006.
  • Jahangiri, M., Rahimi, A. (2012). Relative Cohen-Macaulayness and relative unmixedness of bigraded modules. J. Commut. Algebra. 4(4):551–575. DOI: 10.1216/JCA-2012-4-4-551.
  • Kaplansky, I. (1974). Commutative Rings. Revised ed. Chicago, Ill.-London: The University of Chicago Press.
  • Khashyarmanaesh, K., Salarian, Sh., Zakeri, H. (1997). On the flat dimension of certain modules of generalized fractions. Math. J. Toyama Univ. 20:79–90.
  • Lyubeznik, G. (1984). On the local cohomology modules Hai(R) for ideals a generated by monomials in an R-sequence. In Complete Intersections (Acireale, 1983), Lecture Notes in Math., vol. 1092. Berlin: Springer, pp. 214–220.
  • Rahimi, A. (2010). Relative Cohen-Macaulayness of bigraded modules. J. Algebra. 323(6):1745–1757. DOI: 10.1016/j.jalgebra.2009.11.026.
  • Rahro Zargar, M. (2019). Relative canonical modules and some duality results. Algebra Colloq. 26(2):351–360. DOI: 10.1142/S1005386719000269.
  • Rahro Zargar, M. (2015). On the relative Cohen-Macaulay modules. J. Algebra Appl. 14(3):7.
  • Rahro Zargar, M. (2013). Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module. Arch. Math. 100(1):25–34. DOI: 10.1007/s00013-012-0459-y.
  • Rahro Zargar, M., Zakeri, H. (2016). On flat and Gorenstein flat dimensions of local cohomology modules. Can. Math. Bull. 59(2):403–416. DOI: 10.4153/CMB-2015-080-x.
  • Rahro Zargar, M., Zakeri, H. (2015). On injective and Gorenstein injective dimensions of local cohomology modules. Algebra Colloq. 22(spec01):935–946. DOI: 10.1142/S1005386715000784.
  • Schmitt, T., Vogel, W. (1979). Note on set-theoretic intersections of subvarieties of projective space. Math. Ann. 245(3):247–253. DOI: 10.1007/BF01673509.
  • Sharp, R. Y., Zakeri, H. (1982). Modules of generalized fractions. Mathematika. 29(1):32–41. DOI: 10.1112/S0025579300012134.

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