On the subcategories of n-torsionfree modules and related modules

• Dey, Souvik ^[1] ; Takahashi, Ryo ^[2]
  1. [1] University of Kansas

     University of Kansas

     City of Lawrence, Estados Unidos

     
  2. [2] Nagoya University

     Nagoya University

     Naka-ku, Japón

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 113-132
• Idioma: inglés
• DOI: 10.1007/s13348-021-00338-1
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let R be a commutative noetherian ring. Denote by {\textsf{mod }}\,R the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Bridger, by comparing them with n-syzygy modules, and modules satisfying Serre’s condition (\mathrm {S}_n). We mainly investigate closedness properties of the full subcategories of {\textsf{mod }}\,R consisting of those modules.

• Referencias bibliográficas
  • Auslander, M., Bridger, M.: Stable Module Theory, vol. 94. Memoirs of the American Mathematical Society (1969)
  • Avramov, L.L., Martsinkovsky, A.: Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension. Proc. Lond. Math. Soc....
  • Bruns, W., Herzog, J.: Cohen–Macaulay Rings, Revised Edition, Cambridge Studies in Advanced Mathematics, vol. 39. Cambridge University Press,...
  • Dao, H., Takahashi, R.: The radius of a subcategory of modules. Algebra Number Theory 8(1), 141–172 (2014)
  • Dao, H., Takahashi, R.: Classification of resolving subcategories and grade consistent functions. Int. Math. Res. Not. IMRN 1, 119–149 (2015)
  • Dao, H., Kobayashi, T., Takahashi, R.: Burch ideals and Burch rings. Algebra Number Theory 14(8), 2121–2150 (2020)
  • Dutta, S.P.: Syzygies and homological conjectures. In: Hochster, M., Huneke, C., Sally, J. D. (eds.) Commutative Algebra (Berkeley, CA, 1987),...
  • Enochs, E.E., Jenda, O.M.G.: Gorenstein injective and projective modules. Math. Z. 220(4), 611–633 (1995)
  • Evans, E.G., Griffith, P.: Syzygies, London Mathematical Society Lecture Note Series, vol. 106. Cambridge University Press, Cambridge (1985)
  • Faber, E.: Trace ideals, normalization chains, and endomorphism rings. Pure Appl. Math. Q. 16(4), 1001–1025 (2020)
  • Goto, S., Takahashi, R.: Extension closedness of syzygies and local Gorensteinness of commutative rings. Algebras Represent. Theory 19(3),...
  • Holm, H.: Gorenstein homological dimensions. J. Pure Appl. Algebra 189(1–3), 167–193 (2004)
  • Hoshino, M.: Extension closed reflexive modules. Arch. Math. (Basel) 54(1), 18–24 (1990)
  • Iyama, O.: Higher-dimensional Auslander–Reiten theory on maximal orthogonal subcategories. Adv. Math. 210(1), 22–50 (2007)
  • Kobayashi, T., Takahashi, R.: Ulrich modules over Cohen–Macaulay local rings with minimal multiplicity. Q. J. Math. 70(2), 487–507 (2019)
  • Maşek, V.: Gorenstein dimension and torsion of modules over commutative Noetherian rings. Commun. Algebra 20(12), 5783–5812 (2000)
  • Matsui, H., Takahashi, R., Tsuchiya, Y.: When are n-syzygy modules n-torsionfree? Arch. Math. 108(1), 351–355 (2017)
  • Moore, W.F.: Cohomology over fiber products of local rings. J. Algebra 321(3), 758–773 (2009)
  • Nasseh, S., Takahashi, R.: Local rings with quasi-decomposable maximal ideal. Math. Proc. Camb. Philos. Soc. 168(2), 305–322 (2020)
  • Roberts, P.: Two applications of dualizing complexes over local rings. Ann. Sci. École Norm. Sup. (4) 9(1), 103–106 (1976)
  • Sadeghi, A., Takahashi, R.: Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi. Mich. Math. J....
  • Takahashi, R.: Syzygy modules with semidualizing or G-projective summands. J. Algebra 295(1), 179–194 (2006)
  • Takahashi, R.: Classifying resolving subcategories over a Cohen–Macaulay local ring. Math. Z. 273(1–2), 569–587 (2013)
  • Takahashi, R.: Classification of dominant resolving subcategories by moderate functions. Ill. J. Math. 65(3), 597–618 (2021)