Rocky Mountain Journal of Mathematics

Strongly copure projective, injective and flat complexes

Xin Ma and Zhongkui Liu

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Abstract

In this paper, we extend the notions of strongly copure projective, injective and flat modules to that of complexes and characterize these complexes. We show that the strongly copure projective precover of any finitely presented complex exists over $n$-FC rings, and a strongly copure injective envelope exists over left Noetherian rings. We prove that strongly copure flat covers exist over arbitrary rings and that $(\mathcal {SCF},\mathcal {SCF}^\bot )$ is a perfect hereditary cotorsion theory where $\mathcal {SCF}$ is the class of strongly copure flat complexes.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 6 (2016), 2017-2042.

Dates
First available in Project Euclid: 4 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1483520436

Digital Object Identifier
doi:10.1216/RMJ-2016-46-6-2017

Mathematical Reviews number (MathSciNet)
MR3591270

Zentralblatt MATH identifier
1378.16004

Subjects
Primary: 16E05: Syzygies, resolutions, complexes 16E10: Homological dimension 16E30: Homological functors on modules (Tor, Ext, etc.)

Keywords
Strongly copure projective complex strongly copure injective complex strongly copure flat complex

Citation

Ma, Xin; Liu, Zhongkui. Strongly copure projective, injective and flat complexes. Rocky Mountain J. Math. 46 (2016), no. 6, 2017--2042. doi:10.1216/RMJ-2016-46-6-2017. https://projecteuclid.org/euclid.rmjm/1483520436


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