On the new intersection theorem for totally reflexive modules

• Autores: Kamran Divaani-Aazar, Fatemeh Mohammadi Aghjeh Mashhad, Ehsan Tavanfar, Massoud Tousi
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 3, 2020, págs. 369-381
• Idioma: inglés
• DOI: 10.1007/s13348-019-00264-3
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • André, Y.: La conjecture du facteur direct. Publ. Math. Inst. Hautes Études Sci. 127(1), 71–93 (2018)
  • Asgharzadeh, M.: On the dimension of syzygies. Mathematics. arXiv:1705.04952
  • Auslander, M.: Anneaux de Gorenstein, et torsion en algèbre commutative, Séminaire d’Algèbre Commutative dirigé par Pierre Samuel, 1966/67....
  • Auslander, M., Bridger, M.: Stable Module Theory, Memoirs of the American Mathematical Society, 94. American Mathematical Society, Providence...
  • Avramov, L.L.: Homological Dimensions and Related Invariants of Modules Over Local Rings, Representations of Algebras, I, II, 1–39. Beijing...
  • Avramov, L.L., Gasharov, V.N., Peeva, I.V.: Complete intersection dimension. Inst. Hautes Études Sci. Publ. Math. 86, 67–114 (1997)
  • Avramov, L.L., Martsinkovsky, A.: Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension. Proc. London Math. Soc....
  • Bruns, W., Herzog, J.: Cohen–Macaulay Rings, Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge (1993)
  • Christensen, L.W.: Gorenstein Dimensions. Lecture Notes in Mathematics, vol. 1747. Springer, Berlin (2000)
  • Christensen, L.W.: Semi-dualizing complexes and their Auslander categories. Trans. Am. Math. Soc. 353(5), 1839–1883 (2001)
  • Christensen, L.W., Foxby, H-B., Holm, H.: Beyond Totally Reflexive Modules and Back: A Survay on Gorenstein Dimensions, Commutative Algebra–Noetherian...
  • De Stefani, A., Huneke, C., Núñez-Betancourt, L.: Frobenius Betti numbers and modules of finite projective dimension. J. Commut. Algebra 9(4),...
  • Divaani-Aazar, K., Mohammadi Aghjeh Mashhad, F., Tousi, M.: On the existence of certain modules of finite Gorenstein homological dimensions....
  • Foxby, H.-B.: Bounded complexes of flat modules. J. Pure Appl. Algebra 15(2), 149–172 (1979)
  • Goto, S., Hayasaka, F., Takahashi, R.: On vanishing of certain Ext modules. J. Math. Soc. Jpn. 60(4), 1045–1064 (2008)
  • Hochster, M.: The equicharacteristic case of some homological conjectures on local rings. Bull. Am. Math. Soc. 80(4), 683–686 (1974)
  • Hochster, M.: Topics in the homological theory of modules over commutative rings, CBMS Reg. Conference Series Mathematics. American Mathematical...
  • Nasseh, S., Sather-Wagstaff, S.: Vanishing of Ext and Tor over fiber products. Proc. Am. Math. Soc. 145(11), 4661–4674 (2017)
  • Nasseh, S., Takahashi, R.: Local rings with quasi-decomposable maximal ideal. Mathematical Proceedings of Cambridge Philosophical Society....
  • Nasseh, S., Takahashi, R., Sather-Wagstaff, S., VandeBogert, K.: Applications and homological properties of local rings with decomposable...
  • Ogoma, T.: Existence of dualizing complexes. J. Math. Kyoto Univ. 24(1), 27–48 (1984)
  • Peskine, C., Szpiro, L.: Dimension projective finie et cohomologie locale. Applications à la démonstration de conjectures de M. Auslander,...
  • Roberts, P.: Multiplicities and Chern Classes in Local Algebra, Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (1998)
  • Sather-Wagstaff, S.: Complete intersection dimensions for complexes. J. Pure Appl. Algebra 190(1–3), 267–290 (2004)
  • Strooker, J.R.: Homological questions in local algebra, London Mathematical Society Lecture Note Series, 145. Cambridge University Press,...
  • Stückrad, J., Vogel, W.: Buchsbaum Rings and Applications. An Interaction Between Algebra, Geometry and Topology. Springer, Berlin (1986)
  • Takahashi, R.: On G-regular local rings. Commun. Algebra 36(12), 4472–4491 (2008)
  • Takahashi, R.: The existence of finitely generated modules of finite Gorenstein injective dimension. Proc. Am. Math. Soc. 134(11), 3115–3121...
  • Takahashi, R.: Some characterizations of Gorenstein local rings in terms of G-dimension. Acta Math. Hungar. 104(4), 315–322 (2004)