Home Mathematics Restricted injective dimensions over local homomorphisms
Article
Licensed
Unlicensed Requires Authentication

Restricted injective dimensions over local homomorphisms

  • Dejun Wu EMAIL logo and Fangdi Kong
Published/Copyright: May 18, 2018
Become an author with De Gruyter Brill

Abstract

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.


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



wudj@lut.cn

Communicated by Miroslav Ploščica


Acknowledgement

It is a pleasure to thank the referee for thorough and valuable comments which improve the presentation of the paper.

References

[1] Avramov, L. L.—Foxby, H-B.—Herzog, B.:Structure of local homomorphisms, J. Algebra 164 (1994), 124–145.10.1006/jabr.1994.1057Search in Google Scholar

[2] Avramov, L. L.—Iyengar, S.—Miller, C.: Homology over local homomorphisms, Amer. J. Math. 128 (2006), 23–90.10.1353/ajm.2006.0001Search in Google Scholar

[3] Bennis, D.—Mahdou, N.: First, second, and third change of rings theorems for Gorenstein homological dimensions, Comm. Algebra 38 (2010), 3837–3850.10.1080/00927870903286868Search in Google Scholar

[4] Christensen, L. W.—Foxby, H-B.—Frankild, A.: Restricted homological dimensions and Cohen-Macaulayness, J. Algebra 251 (2002), 479–502.10.1006/jabr.2001.9115Search in Google Scholar

[5] Foxby, H-B.: Hyperhomological algebra & commutative rings, in preparation.Search in 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. 119–137.10.1090/conm/331/05906Search in Google Scholar

[7] Iyengar, S.—Sather-Wagstaff, S.: G-dimension over local homomorphisms. Applications to the Frobenius endomorphism, Illinois J. Math. 48 (2004),241–272.10.1215/ijm/1258136183Search in Google Scholar

[8] Takahashi, R.: The existence of finitely generated modules of finite Gorenstein injective dimension, Proc. Amer. Math. Soc. 134 (2006), 3115–3121.10.1090/S0002-9939-06-08428-0Search in Google Scholar

[9] Wu, D.: Gorenstein dimensions over ring homomorphisms, Comm. Algebra 43 (2015), 2005–2028.10.1080/00927872.2014.881836Search in Google Scholar

[10] Wu, D.—Liu, Z.: On restricted injective dimensions of complexes, Comm. Algebra 41 (2013), 462–470.10.1080/00927872.2012.656339Search in Google Scholar

[11] Yassemi, S.: A generalization of a theorem of Bass, Comm. Algebra 35 (2007), 249–251.10.1080/00927870601041672Search in Google Scholar

Received: 2015-10-5
Accepted: 2016-12-20
Published Online: 2018-5-18
Published in Print: 2018-6-26

© 2018 Mathematical Institute Slovak Academy of Sciences

Downloaded on 15.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0136/html
Scroll to top button