## 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.

Show Summary Details# Restricted injective dimensions over local homomorphisms

## Abstract

## References

## About the article

More options …# Mathematica Slovaca

More options …

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year

IMPACT FACTOR 2017: 0.314

5-year IMPACT FACTOR: 0.462

CiteScore 2017: 0.46

SCImago Journal Rank (SJR) 2017: 0.339

Source Normalized Impact per Paper (SNIP) 2017: 0.845

Mathematical Citation Quotient (MCQ) 2017: 0.26

- Online
- ISSN
- 1337-2211

Dejun Wu / Fangdi Kong

30,00 € / $42.00 / £23.00

Get Access to Full TextIn 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

**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.

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.