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Title: $n$-flat and $n$-FP-injective modules (English)
Author: Yang, Xiaoyan
Author: Liu, Zhongkui
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 61
Issue: 2
Year: 2011
Pages: 359-369
Summary lang: English
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Category: math
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Summary: In this paper, we study the existence of the $n$-flat preenvelope and the $n$-FP-injective cover. We also characterize $n$-coherent rings in terms of the $n$-FP-injective and $n$-flat modules. (English)
Keyword: $n$-flat module
Keyword: $n$-FP-injective module
Keyword: $n$-coherent ring
Keyword: cotorsion theory
MSC: 13C11
MSC: 13D07
MSC: 16D40
MSC: 16E10
idZBL: Zbl 1249.13011
idMR: MR2905409
DOI: 10.1007/s10587-011-0080-4
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Date available: 2011-06-06T10:28:23Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/141539
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Reference: [1] Aldrich, S. T., Enochs, E. E., Rozas, J. R. García, Oyonarte, L.: Covers and envelopes in Grothendieck categories: Flat covers of complexes with applications.J. Algebra 243 (2001), 615-630. MR 1850650, 10.1006/jabr.2001.8821
Reference: [2] Chase, S. U.: Direct products of modules.Trans. Am. Math. Soc. 97 (1961), 457-473. Zbl 0100.26602, MR 0120260, 10.1090/S0002-9947-1960-0120260-3
Reference: [3] Chen, J., Ding, N.: On $n$-coherent rings.Commun. Algebra 24 (1996), 3211-3216. Zbl 0877.16010, MR 1402554, 10.1080/00927879608825742
Reference: [4] Ding, N.: On envelopes with the unique mapping property.Commun. Algebra 24 (1996), 1459-1470. Zbl 0863.16005, MR 1380605, 10.1080/00927879608825646
Reference: [5] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra.de Gruyter Expositions in Mathematics, 30 Walter de Gruyter Berlin (2000). Zbl 0952.13001, MR 1753146
Reference: [6] Lee, S. B.: $n$-coherent rings.Commun. Algebra 30 (2002), 1119-1126. Zbl 1022.16001, MR 1892593, 10.1080/00927870209342374
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