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Mathematica Slovaca

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Volume 68, Issue 3


Restricted injective dimensions over local homomorphisms

Dejun Wu / Fangdi Kong
Published Online: 2018-05-18 | DOI: https://doi.org/10.1515/ms-2017-0136


In this paper, we study the small restricted injective dimension over local ring homomorphisms. Some of known results are generalized. For example, the Bass formula for the small restricted injective dimension of complexes is extended.

MSC 2010: Primary 13D05, 13D02

Keywords: Cohen factorization; the small restricted injective dimension; width of complex

The research has been supported by National Natural Science Foundation of China (No. 11761047).


  • [1]

    Avramov, L. L.—Foxby, H-B.—Herzog, B.:Structure of local homomorphisms, J. Algebra 164 (1994), 124–145.CrossrefGoogle Scholar

  • [2]

    Avramov, L. L.—Iyengar, S.—Miller, C.: Homology over local homomorphisms, Amer. J. Math. 128 (2006), 23–90.CrossrefGoogle Scholar

  • [3]

    Bennis, D.—Mahdou, N.: First, second, and third change of rings theorems for Gorenstein homological dimensions, Comm. Algebra 38 (2010), 3837–3850.CrossrefGoogle Scholar

  • [4]

    Christensen, L. W.—Foxby, H-B.—Frankild, A.: Restricted homological dimensions and Cohen-Macaulayness, J. Algebra 251 (2002), 479–502.CrossrefGoogle Scholar

  • [5]

    Foxby, H-B.: Hyperhomological algebra & commutative rings, in preparation.Google Scholar

  • [6]

    Foxby, H-B.—Iyengar, S.: Depth and amplitude for unbounded complexes. Commutative Algebra (Grenoble/Lyon, 2001) (Providence, RI), Contemp. Math., Vol. 331, Amer. Math. Soc., 2003, pp. 119–137.Google Scholar

  • [7]

    Iyengar, S.—Sather-Wagstaff, S.: G-dimension over local homomorphisms. Applications to the Frobenius endomorphism, Illinois J. Math. 48 (2004),241–272.Google Scholar

  • [8]

    Takahashi, R.: The existence of finitely generated modules of finite Gorenstein injective dimension, Proc. Amer. Math. Soc. 134 (2006), 3115–3121.CrossrefGoogle Scholar

  • [9]

    Wu, D.: Gorenstein dimensions over ring homomorphisms, Comm. Algebra 43 (2015), 2005–2028.CrossrefGoogle Scholar

  • [10]

    Wu, D.—Liu, Z.: On restricted injective dimensions of complexes, Comm. Algebra 41 (2013), 462–470.CrossrefGoogle Scholar

  • [11]

    Yassemi, S.: A generalization of a theorem of Bass, Comm. Algebra 35 (2007), 249–251.Google Scholar

About the article

Received: 2015-10-05

Accepted: 2016-12-20

Published Online: 2018-05-18

Published in Print: 2018-06-26

Citation Information: Mathematica Slovaca, Volume 68, Issue 3, Pages 691–697, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0136.

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